Citation
Use of Impedance Spectroscopy to Investigate Factors That Influence the Performance and Durability of Proton Exchange Membrane (PEM) Fuel Cells

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Title:
Use of Impedance Spectroscopy to Investigate Factors That Influence the Performance and Durability of Proton Exchange Membrane (PEM) Fuel Cells
Creator:
Roy, Sunilkumar
Place of Publication:
[Gainesville, Fla.]
Publisher:
University of Florida
Publication Date:
Language:
english
Physical Description:
1 online resource (180 p.)

Thesis/Dissertation Information

Degree:
Doctorate ( Ph.D.)
Degree Grantor:
University of Florida
Degree Disciplines:
Chemical Engineering
Committee Chair:
Orazem, Mark E.
Committee Members:
Weaver, Jason F.
Hagelin-Weaver, Helena E.
Wachsman, Eric D.
Graduation Date:
8/9/2008

Subjects

Subjects / Keywords:
Anodes ( jstor )
Capacitance ( jstor )
Cathodes ( jstor )
Current density ( jstor )
Electrodes ( jstor )
Fuel cells ( jstor )
Hydrogen ( jstor )
Parametric models ( jstor )
Reactants ( jstor )
Standard deviation ( jstor )
Chemical Engineering -- Dissertations, Academic -- UF
capacitance, drying, flooding, fuel, impedance, peroxide, pto, stochastic
Genre:
Electronic Thesis or Dissertation
born-digital ( sobekcm )
Chemical Engineering thesis, Ph.D.

Notes

Abstract:
Impedance spectroscopy provides the opportunity for in-situ identification and quantification of physical processes and has been used extensively to study the behavior of the fuel cell. However, a key question to be answered is whether the features seen in the impedance response are caused by an artifact or represent a physical process taking place in the system. The measurement model developed by our group can be used to identify the frequency ranges unaffected by bias errors associated with instrument artifacts and non-stationary behavior. Impedance measurements were performed with the 850C fuel-cell test station supplied by Scribner Associates and with a Gamry Instruments FC350 impedance analyzer coupled with a Dynaload electronic load. All electrochemical measurements were performed with a two-electrode cell in which the anode served as a pseudo-reference electrode. The experiments were conducted in galavanostatic mode for a frequency range of 0.001-3000 Hz with 10 mA peak-to-peak sinusoidal perturbation, and ten points were collected per frequency decade. Ultra pure hydrogen was used as the anode fuel, and compressed air was used as oxidant. The measurement model was used to show that low-frequency inductive loops were, in some cases, fully self consistent, and, therefore, the inductive loops could be attributed to processes occurring in the fuel cell. Then we developed first-principle models that incorporate processes that may be responsible for the inductive response seen at low frequencies. We found that side reactions producing hydrogen peroxide intermediates and reactions causing Pt deactivation could yield inductive loops. These side reactions and the intermediates can degrade fuel cell components such as membranes and electrodes, thereby reducing the lifetime the fuel cells. The evidence of peroxide and Pt dissolution in our system by microstructural characterization was validated. In addition, a more sensitive manner of using impedance spectroscopy to gain an insight into the problem of flooding which adversely affects the performance of the fuel cell was established. A comprehensive model for base-level noise in impedance measurements for normal (non-flooded) conditions was developed and actual noise in flooded conditions was calculated by transient fixed-frequency measurements. A comparison of the actual noise to the base-level noise was used to detect onset of flooding. Also, graphical methods were used to interpret impedance spectra in terms of interfacial capacitance. The effective interfacial capacitance decreased with increase in current and decreased slowly with time. The decreases in interfacial capacitance with higher current density can be attributed to an excess amount of water i.e., flooding; whereas, the decrease in interfacial capacitance with time may be related to catalyst dissolution and deactivation. ( en )
General Note:
In the series University of Florida Digital Collections.
General Note:
Includes vita.
Bibliography:
Includes bibliographical references.
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Description based on online resource; title from PDF title page.
Source of Description:
This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Thesis:
Thesis (Ph.D.)--University of Florida, 2008.
Local:
Adviser: Orazem, Mark E.
Electronic Access:
RESTRICTED TO UF STUDENTS, STAFF, FACULTY, AND ON-CAMPUS USE UNTIL 2010-08-31
Statement of Responsibility:
by Sunilkumar Roy.

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Source Institution:
University of Florida
Holding Location:
University of Florida
Rights Management:
Copyright Roy, Sunilkumar. Permission granted to the University of Florida to digitize, archive and distribute this item for non-profit research and educational purposes. Any reuse of this item in excess of fair use or other copyright exemptions requires permission of the copyright holder.
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8/31/2010
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temperature fuel-cell applications,234 tO Study the effect of temperature on resistance

and proton conductivity of composite membranes,353 to measure ionic and electronic

resistibility of composite electrode catalyst for the fuel cell application."' Using the

impedance, Li et al."'5 have investigated a reference electrode to resolve effects at the

anode and cathode and within the membrane the fuel cell.

The object of this chapter is to provide a comprehensive analysis of performance of

the fuel cell in terms of impedance and polarization results as a function of several factors.

The factors an~ lli-. I1 include operating conditions such as current density, temperature,

and backpressure, and design parameters such as flow channels, and GDLs. Brief of

techniques, methods, and materials used is also presented.

3.2 Experimental

The experimental system and the impedance instrumentation used are presented in

this section.

3.2.1 Materials and Chemicals

The MEA (purchased from lon Power, Inc., New Castle, DE) emploi- al 0.0508 mm

(2 mils) thick Nafion N112 with catalyst 1... ris of about 0.025 mm on both sides of the

membrane. The active surface area was 5 cm2. One more MEA with the same thickness of

the membrane, and < lI I1i--r but embeded GDL hoth side of the catalyst 1.,-c rs was used

which was supplied by fuelcellstore (San Diego, CA). The catalyst 1 e -;- rs were platinum

supported on carbon with a Pt catalyst loading of 0.4 mg/cm2 on both the anode and

the cathode sides. Two types of GDL were used during assembling the MEA. Both

have an effective thickness of 0.284 mm, and were made of carbon cloth, but one was

uniformly macro-porous while the other has variable porosity. The nonuniform GDL was

micro-porous to the catalyst side and macro-porous to the channel side. Similar GDL

structures have been reported in the literature.64-66 The material of the flow channel (

flow configurations are shown in Figure 3-1) used was made of graphite with the outlet

lower than the inlet to facilitate removal of condensed water. Hydrogen gas was used as










LIST OF TABLES


Table page

5-1 Parameters used to calculate the impedance response corresponding to Models
1, 2, and 3. ...... ...... ........... 103



















(a)I (b)

Fiue64 TMiae o rs-ecin E tuywsprfre ih OLJM









siurfae area has also bee atributsedtion the pltiumy dissproluio d reepsiin at the SM




catalyst/ectrolyte interface foo The migration of the platinum particles to the membrane

interface has also been reported.94 Once the catalyst particle has migrated into the

membrane, it would lose the electrical contact from the catalyst 1 .-;
cause the loss of the electrochemical active surface area.

The SENT images of MEA cross sections are presented in Figure 6-5, in which the

morphology changes in the interface of electrode-membrane can he clearly seen. CI Ing.-

in surface features was observed in the SENT images of surface the fresh (Figure 6-5(a))

and the used (Figure 6-5(b)) catalyst 1.i;< c. These type of changes have been described as

mud-cracking and surface erosion and have been explained as a result of catalyst particle

or recast Nafion ionomer loss from the catalyst surface due to particle dissolution.'ot

6.3.2 Ef~uent Analysis

ICP-MS was used to analyze the effluent from the cathode of the fuel cell under

operation at different points along the polarization curve. A trace amount of Pt was









with


Eo = 0.98 0.059pH (2-18)

and

PtO + H20 PtO2 + 2H+ + 2e- (2-19)

with

Eo = 1.05 0.059pH (2-20)

Pt dissolution in a the fuel cell conditions under potential cycle was investigated and the

solubility of Pt was presented as a function of different factors such as temperature, pH,

and oxygen partial pressure.92 The dissolution reaction was found to be an exothermic

reaction, and solubility of Pt increased with temperature. The solubility increase with

decrease in pH and solubility significantly increases with presence of oxygen in atmosphere

according to:

PtO + n02 + 2H*' + H20 Pt(OH)( (2-21)

The finite solubility of Pt in acidic medium enables its movement into Nafion. The

movement of Pt particles can be accomplished by diffusion, migration and possibly by

convection.93 Pt partiCleS dissolve in catalyst 111-,- r and subsequent .I__-oegated into'?1 .--;i

particles the process is govern by Ostwald ripening. Once particles have grown 1i-.1- 1i- (in

micro-size) they can migrate by diffusion in catalyst 111-;-r and/or into membrane.94 IHSide

the membrane, the movement can also be considered by convection mode. A mathematical

model for Pt movement in membrane is illustrated based on dilute-solution theory though

it has ignored several realistic factors such effect of double-l .>. r charging, convection

Brownian motion of Pt particles, and potential dependency on the charge movement.95

Several other researchers have advocated platinum oxidation and dissolution under

normal the fuel cell operating conditions.87,96-98, 93, 90, 99 Experimental results have also

confirmed coarsening of the Pt particles after 500 hours of operation.100 The platinum

oxidation and dissolution may result in decreases of electrochemically active surface area










where i is current density, io is exchange current density, and a~ is apparent transfer

coefficient.

Activation losses are minimized by maximizing the exchange current density. The

exchange current density is a function of the catalyst material and the electrochemical

active surface area. The electrodes are made highly porous by dispersing, nano-scale

particles of platinum on electronic conductor porous carbon support mixed with an ion

conductive electrolyte to enhance the overall active area.

2.1.2 Ohmic Potential Loss

Ohmic losses arise due to the resistance of the materials (electrodes, membrane) to

flow of species such as proton transport through the membrane and electrodes, electron

transport through electrodes, bipolar plates, and collector plates. It appears as a linear

part in the middle of polarization curve. The magfnitudes of these potential losses depend

on the materials used in the construction of the fuel cell and the operating conditions of

the cell. Most of the ohmic loss arises from the ionic resistance in the electrolyte. The

thinner the membrane, the lower this loss. Thinner membranes are also advantageous

because they keep the anode electrode wet by back-diffusion of water from the cathode,

however very thin membrane could lead to pinhole formation and therefore gas crossover.

It is also reported that the interfacial resistance between the gas diffusion 1 e. ;r and

the bipolar plate might contribute significantly to the total ohmic resistance, especially

when alternative bipolar plate materials such as steel are used.l5

2.1.3 Concentration Overpotential Loss

At high current densities, the voltage output of the fuel cell once again drops rapidly

due to mass-transport limitations at the electrodes. The concentration losses can be

evaluated as:

rlcone. = TIn( ) (2-8)

where izim is limiting current densities.










0.225

0.21 ,......--o- ....--o


0.180 ." -




O
0.165 .

0.150 --

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5

Applied Backpressure I barg


Figure 8-9: The interfacial capacitance C nf, obtained from equation (8-2), as a function
of backpressure applied for both the cathode and the anode. The impedance data were
recorded at 0.7 A/cm2 at 70 oC'. The experimental system was the same as described in
Figure 8-1.


at elevated temperatures, which may account partially for the better performance at

higher temperatures.

A similar investigation of the influence of backpressure was performed. The resulting

interfacial capacitance, obtained from equation (8-2), is presented in Figure 8-9 as a

function of backpressure applied for both the cathode and the anode. The impedance data

were recorded at 0.7 A/cm2 at 70 oC'. A significant increase in interfacial capacitance was

observed with an increase in the backpressure from 0 to 2 barg. Subsequent increases in

backpressure resulted in only small increases in interfacial capacitance.

8.2.3 Effect of Design Parameters

Impedance data recorded with different combinations of flow channels and gas-

diffusion 1.,-;-re were also analyzed to estimate the interfacial capacitance as presented in

Figure 8-10. The inter facial capacitance for MEAs assembled using a gas diffusion 1 ... r

with a nonuniform pore distribution was significantly larger than that obtained for MEAs

assembled using a gas diffusion l o,-;- with a uniform pore distribution. This difference

may be attributed to the improved water management properties of the gas diffusion









REFERENCES


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1 1 1 1 1 1 "
,-*^

--0--0.2 A cm-2Ser
pentine


0.80


0.75 ~ _-w -a r *2 Itriia
&- 1.02 A cm-2, Interdigitated
0.70 .-~-0.4 A cm-2, Interdigitated




0.60 o~4;,~~-----------o0-----------o------

0.55 IIIIIi
0.5 1.0 1.5 2.0 2.5 3.0 3.5

Time /h

Figure 8-12: CPE exponent a~ Interfacial-capacitance as a function of time corresponding
to the results presented in Figure 8-11.


response. The advantage of the graphical methods emploi- a here is that the parameter

values do not depend on the suitability of the model and on the quality of the regression.

The values of the CPE parameters Q and a~ can be obtained unequivocally, however, the

relationship between these parameters and the interfacial capacitance requires a model.

The formulas developed by Brug et al.227 WeTO found to give good accounting for 2-D

distributions."I1 A similar verification has not been provided for 3-D distributions, though

the Brug formula has been invoked to describe the relationship between CPE parameters

and 3-D distributions in oxides.228

The values of a~ was found in the present work to range between 0.57-0.8, which is

consistent with the value of 0.8027 reported by Fouquet et al.1s7 The value of a~ can be

expected to result from a combined lateral distribution, associated with the distribution

of current and potential along the flow channels and between land and channel areas, and

an axial distribution associated with the porous character of the MEA. The decreased

value of a~ at low and high current densities may be attributed to increased heterogeneity

created by drying or flooding, respectively. Correspondingly, a decrease in the value of Ceaf

was found under conditions associated with drying and flooding. The calculated interfacial










[189] M. N. Tsampas, A. Pikos, S. Brosda, A. K~atsaounis, and C. G. V...i-s .!- "The Effect
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(2006) 2743-2755.

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J. J. Fontanella, S. Suarez, and S. G. Greenbaum, "C'I I) Il:terization of Electro-
;11l-p ... Nafion Films," Journal of Power Sources, 129 (2004) 55-61.

[191] F. Liu, B. Yi, D. Xing, J. Yu, Z. Hou, and Y. Fu, "Development of Novel Self-
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Sectional Samples of Proton Exchange Membrane Fuel Cells by Ultramicrotomy for
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Mathematical Models," Journal of the Electrochemical S -. .:. Iri, 151 (2004) A311-
A,325.

[196] F. Y. Zlr Ilr_ X. G. Yang, and C. Y. Wang, "Liquid water removal from a PEM fuel
cell," Journal of the Electrochemical S8... .:. Iri, 153 (2006) A225-A232.

[197] X. C!. is,~ J. Z1!I. .1 Y. Tang, C. Song, J. Shen, D. Song, and J. Zhang, "Hydrogen
crossover in high-temperature PEM fuel cell," Journal of Power Sources, 167 (2007)
25-31.

[198] M. C. Leverett, "Capillary Behavior in porous solid," in Pet. Trans. AIM~E, volume
142 (1941) 152.

[199] X. Li and I. Sabir, "Review of Bipolar Plates in PEM Fuel Cells: Flow-Field
Designs," International Journal of H;;Jri,. e.I Energy, 30 (2005) 359- 371.

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Solid State Electrochem, 7 (2003) 651-657.









6.3.1 Microstructural Characterization

The full-scan XPS spectra is presented in Figure 6-1. It was discerned that the peak

intensities of F, C was reduced in the used sample whereas the intensities of Pt and O

were enhanced. The amount of carbon could decrease due to corrosion and enhanced

amount of oxygen can be ascribed to surface oxidation of Pt in electrodes. An increase

in the elemental composition of Pt and O was noticed in the used MEA, which could

support the formation of PtO in the used MEA. A peak of PtO was detected in the

spectra of used sample was recorded in during XPS investigation as shown in Figure 6-2.

The analysis of spectra presented in Figure 6-2 were performed by 11 point, 2nd order,

Savitsky-Golay smoothing followed by a Shirley background subtraction. This set the

ends of the spectrum to a zero baseline and then the spectra were normalized. The two

spectra were imported obtained from clean Pt(100) and 3 ML (n1.~r~l ir..1 r) of atomic

oxygen on Pt(100) from data presented by Shumbera et al.220 XPS data does indicate

oxide formation in the 1 to 3 ML range.

It is worth noting that the Pt 4f shoulder from the 3 ML oxide is small because the

electron kinetic energy for that peak is large ( 1300 eV) when using a laboratory X-ray

source which may be due to reduced surface sensitivity at lower binding energy.

TEM was applied to study .......1. ..~ 11; li..i of catalyst particles, high-resolution TEM

monograms presented in Figure 6-3 have showed '?1 r-i Pt particle size in case of used

MEA as compared to fresh one. In the TEM images of cross-section of MEAs migration

of Pt particles from cathode-membrane interface to membrane was observed. The TEM

image of cross-section of fresh and used MEAs are presented in Figure 6-4. C'!s Iass. in

interface of the catalyst-membrane were evident.

The decrease in the surface area could be due to combined effect'o1 of (i) metal

catalyst cluster ..-z-oluin ~! 11;..!: or (ii) loss of support particles and metal cluster from

the catalyst 1.>. -r. Due to weak bonding of platinum particles with the carbon support,

the formation of .-ol__in,!~ I .1es of the catalyst particles are possible. The decreased









c =1./C;

thetal = (b + sqrt(b.2 + 4. c. a))./(2 + a);

ih2 = (A. ilimb2)./(A + ilimb2); figure(2)plot(ih2, V,' +');

io2 = (B. ilimo2. (1 theta2))./((B. (1 theta2)) + ilimo2);

ih2o2 = (C. ilimb2o2. + theta2)./((C. + theta2) + ilimb2o2);

iT = ih2 + io2 + ih2o2; [Total current]

w = -6 : .05 : 6; [Frequency range]

w =10.";

Kh2 = (w + delta2)/dh2; bh2 = tanh(sgrt(i + Kh2))./(sgrt(i + Kh2));

Ko02 = (w. + delta2)/do2; bo2 = tanh(sgrt(i + Ko2))./(sgrt(i + Ko2));

K~h2o2 = (w. + delta2)/dh2o2;

b2o2 = tanh(sgrt(i + Kh2o2))./(sgrt(i + Kh2o2));

Ci = 1./(RtH2 + ZDH2 + bh2);

D1 = 1./(RtO2 + ZDO2 + bo2);

D2 = 1./((RtO2 + ZDO2 + bo2). (1 -i~,,,,,,,**));

El = 1./(RtH202 + ZDH202 + b2o2);

E2 = 1./((RtH202 + ZDH202 + b2o2). -to let*****);

H = (D2 E2). (D1 E1)./(2 + 96500 + i + 2 + 3.14 w D2 + E2);
z=re +(1./((C1+ D1+ E1)+ H +(i s 2 +3.14t w ~c))) +(1./((C1) +(i s2 +3.14 t w ~c)));

zr = real (z);

zi = imag(z);









APPENDIX C: COMPUTATIONAL ALGORITHM FOR MODEL 3

rl = 0.135; [Electrolyte resistance]

c = 0.212; [Double-l} u. r capacitance]

cto = 0.5 [symmetry coefficient for ORR]

as = (1 Qo); [symmetry coefficient for HOR]

V = 0.68; [operating voltage]

F = 96500; [Farel-lli constant]

R = 8.314; [Universal gas constant]

T = 298; [Temperature]

ko = 2.63 +10-2; [Rate constant for ORR]

kh = 3.6 10-4; [Rate constant for HOR]

O = ko s exzp(-(caoFV)/(RT)); [K~inetic expression for ORR]

H = kh & exzp(-(caaFV)/(RT)); [K~inetic expression for HOR]

Y = [O/(O + H)]; [Surface coverage of hydrogen peroxide]
A = 2. Kh2. F. Dh2. Ombulkh2. exz~(bh2. vb2);

k1 = 4. F. Do2. Ombulko2. exz~(-bo2. vo2);

Cl = Ktf. +exp(bpt. +vpt);

C2 = -Kptb. exzp(-bpt. vpt); k2 = C1 C2 + k3;

a = (Kpt. k1. (ilimo2 + C1)) + (C1. ilimo2);
b = -((Kpt. k1. (ilimo2 + k2)) + ((k2 (Kpto. kl)). ilimo2));

c = (k2. kl). (Kpt Kpto);

thetal = (b + sqrt((b.2) (4. c. a)))./(2 + a);

theta2 = C1./(k2); figure(1)plot(V~ theta2);

ih2 = (A. ilimb2)./(A + ilimb2);

Ke = Kpt + ((Kpto Kpt). + theta2);

B = Ke. kl; io2 = (B. ilimo2)./(B + ilimo2);

ip~t = (C1. I (1 theta2)) (C2. + theta2);











1.0-


> 0.8-


a,0.6-


0.4-

0.0 0.2 0.4 0.6 0.8

Current Density / A cm-2

Figure :3-2: Polarization curves recorded with the 850C for an interdigitated channel as a
function of current densities at the cell temperature 40 oC. The anode and the cell tem-
peratures were set at 40 oC and the cathode temperature at :35 op.


peaks were performed at pass energy of 22.36 eV. The atoms were assigned according to

finding energy of visible peaks and atomic composition of elements were evaluated hv

relatives intensities of the peaks.

3.3 Results

Steady-state measurements (polarization curves) and impedance responses of the fuel

cell are presented as a function of different operating parameters.

3.3.1 Current Density as a Parameter

Impedance measurements were performed at several points along the polarization

curve presented in Figure :3-2. Two different trends in the impedance response were

observed. As shown in Figure :3-3, the impedance decreased with increasing current

density for low current density (i < 0.5 A/cm2 ). As shown in Figure :3-3, the impedance

increased with increasing current density for high current density (i > 0.5 A/cm2). These

trends are consistent with changes in the slope of the polarization curve with current

density. It was found that the impedance was the lowest in case of intermediate current

followed by the lower current and the impedance was found the highest at the higher

current of the fuel cell, which was consistent with our previous findingfs.194










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Siloxane on the Catalytic Activity of Pt on Carbon," Electrochemical and Solid-State
Letters, 10 (2007) B207-B209.

[104] R. Mohtadi, W. K(. Lee, and J. W. V. Zee, "Assessing Durability of Cathode
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225.

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[106] M. Ciureanu and H. Wang, "Electrochemical Impedance Study of Electrode-
Membrane Assemblies in PEM Fuel Cells: I. Electro-oxidation of H2 and H2/CO
Mixtures on Pt-Based Gas-Diffusion Electrodes," Journal of the Electrochemical
S8 .. .:. Iri, 146 (1999) 4031-4040.

[107] M. Ciureanu, S. D. Mikhailenko, and S. K~aliaguine, "PEM Fuel Cells as Membrane
Reactors: K~inetic Analysis by Impedance Spectroscopy," Corlrlet;,; T../.7 i, 82 (2003)
195-206.

[108] N. Wagner, W. Schnurnberger, B. Muller, and M. Lang, "Electrochemical Impedance
Spectra of Solid Oxide Fuel Cells and Polymer Membrane Fuel Cells," Electochimica
Acta, 43 (1998) 3785-3793.

[109] J. Fleig, P. Pham, P. Sztulzaft, and J. Maier, "Inhomogeneous Current Distributions
at Grain Boundaries and Electrodes and Their Impact on the Impedance," Solid
State lonics, 113-115 (1998) 739-747.

[110] K(. Sasaki, Y. Hori, R. K~ikuchi, K(. Eguchi, A. Ueno, H. Takeuchi, M. Aizawa,
K(. Tsujimoto, H. Tajiri, H. Nishikawa, and Y. Uchida, "Current-Voltage ('I! I) II:-
teristics and Impedance Analysis of Solid Oxide Fuel Cells for Mixed H2 and CO
Gases," Journal of the Electrochemical So .:. Iri, 149 (2002) A227-A233.

[111] A. Barbucci, R. Bozzo, G. Cerisola, and P. Costamagn, "('ll lI Il:terisation of
Composite SOFC Cathodes using Electrochemical Impedance Spectroscopy. Analysis
of Pt/YSZ and LSM/YSZ Electrodes," Electochimica Acta, 47 (2002) 2183-2188.

[112] M. J. Jurgensen, S. Primdahl, and M. Mogensen, "('I! I) Il:terisation of Composite
SOFC Cathodes Using Electrochemical Impedance Spectroscopy," Electochimica
Acta, 44 (1999) 4195-4201.

[113] S. McIntosh, S. B. Adler, J. M. Vohs, and R. J. Gorte, "Effect of Polarization
on and Implications for ('ll I) Il:terization of LSM-YSZ Composite Cathodes,"
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[114] J. T. Mueller and P. M. Urban, "('I! I) Il:terization of Direct Methanol Fuel Cells by
AC Impedance Spectroscopy," Journal of Power Sources, 75 (1998) 139-143.










7-15 Normalized standard deviations for the real part of the impedance measured at
0.1 Hz for fuel cells containing two different MEAs as a function of current den-
sity. The experiments for the uniform MEA were performed at 50 oC, and the
experiments for the nonuniform MEA were performed at 70 oC. .. .. .. .. 137

8-1 Impedance response recorded at 70 oC with current density as a parameter. The
fuel cell was assembled with a non-uniform GDL and an interdigfitated flow chan-
nel............... .. ...... ..139

8-2 Representation of the graphical analysis of the data presented in Figure 8-1 to
obtain the CPE exponent a~: a) the magnitude of the imaginary part of the impedance
as a function of frequency with current density as a parameter; and b) CPE ex-
ponent obtained from the slope of part (a) at high frequencies. .. .. .. .. 140

8-3 Representation of the graphical analysis of the data presented in Figure 8-1 to
obtain the CPE coefficient Qeaf and the interfacial capacitance Cenf: a) CPE co-
efficient obtained from equation (8-1); and b) the interfacial capacitance ob-
tained from equation (8-2). ......... .. .. 141

8-4 CPE coefficient Qeaf as a function of current density with time as a parameter.
The impedance data were obtained under the conditions described for Figure 8-1. 142

8-5 The interfacial capacitance Ceaf, obtained from equation (8-2), as a function of
current density with time as a parameter. The impedance data were obtained
under the conditions described for Figure 8-1. .... ... .. 142

8-6 Electrochemical parameters obtained for the data presented in Figures 8-4 and
8-5 as a function of current density with time as a parameter: a) CPE expo-
nent a~; and b) Ohmic resistance Re. . .... .. 143

8-7 Impedance response recorded at a current density of 0.5 A/cm2 With system
temperature as a parameter. The experimental system was the same as described
in Figure 8-1. ......... ... .. 144

8-8 The interfacial capacitance Ceaf, obtained from equation (8-2), as a function of
system temperature for the data presented in Figure 8-7. .. .. .. 144

8-9 The interfacial capacitance Ceaf, obtained from equation (8-2), as a function of
backpressure applied for both the cathode and the anode. The impedance data
were recorded at 0.7 A/cm2 at 70 oC. The experimental system was the same
as described in Figure 8-1. . .. ... .. .. 145

8-10 Interfacial capacitance as a function of current density for different combina-
tions of flow channels and gas-diffusion lwi;-r The impedance data were recorded
at 70 0C ... ......... .............. 146

8-11 Interfacial capacitance as a function of time with operating and system con-
dition as a parameter. The impedance data were recorded at 70 oC using an
MEA with a non-uniform GDL. .... ... .. 147









where Kpt is the rate constant on a platinum site and KPto is the rate constant on a

platinum oxide site. The ORR was assumed to take place according to reaction (5-15)

with a steady-state current density given by


io, = ~effo, (0) exp (-bo, ilo, ) (5-43)


where Ken is defined by equation (5-42).

The overall impedance was calculated to be

1 1
Z = Re + + (5-44)
Rt,H2 1ZD,H2 ,a e 2F(jrw K3)+B O
where
1 1 1
Zen + + (5-45)
Rt o, + ZDOs RPt, f RPt,b
(KPto KPt) 1 1 1 1
A = +(-
Keffbo, Ret,fbetyf(1 Y)to) RPt,bbPt,b7PtOI RPt,f Pt,bj 56
and
1 1
B = (5-47)
Ret,fbptyf(1 Ytwo) RPt,bbPt,b7PtO

In equation (5-45), Rtoo, is the charge-transfer resistance for the ORR, i.e..


Rtoo, = [Kedco,(0)bo, exp(-bo,rlo )]- (5-48)


ZD.O, is the nmass-transport impedance for the ORR, i.e..

60 -1
ZD,o o (5-49)
Co?(0)bo 4FDo, Go,(0)

Rptyf is the charge-transfer resistance for the forward reaction, i.e..


Rtpt,p = [KPt,Sbet, (1 rpto) exp(bpat~flptlf)] (5-50)

and RPt,b is the charge-transfer resistance for the backward reaction, i.e..


RPt,b = [KPt,bbPt,b7Pjlto exp(-bPt~b~llPt~gb -1 (5-51)



































I I I I I I I I I I
0.0 0.2 0.4 0.6 0.8 1.0

Current Density / A cm-2


Figure 3-4: Polarization curves recorded as a function of cell temperature by the steady
state measurement with the 850C for H2 as reactant at the anode and air as oxidant at
the cathode. The anode the cathode temperature at were fixed at 70 oC. The fuel cell was
assembled with a serpentine channel.


I 1 1 I I


-g




-




-o
-a


0.8


0.6


0.4


300 C
400 Co
500 Co
600 C o
70 C


-o 1 I-


0 15 0 30 0 45
Z / a cm2


0 60 0 75 0 90


Figure 3-5: Impedance responses as a function of temperature at 0.5 A/cm2 collected with
the 850C with a serpentine channel.


Lb & & o o 0 C
ro o 7
*, a 0



B .aaa a o 700O









In equation (5-29), Rt,O, is the charge-transfer resistance for the first step of the ORR,



Rtoo, = [Ko~co,(0)bo,(1 :iH202) exp(-boa290 2)- (5-32)

ZD,O, iS the mass-transfer impedance for the first step of the ORR, i.e.,

60 -1
ZD,O O (5-33)
Coz (0)bo, 2FDo, 8o,(0)

and Rt,H2O, iS the charge-transfer resistance for the second step of the ORR, i.e.,


ItHO, = [KH20a bH%0O,7HZO, exp-(-bHaO291HO 021-1 (5-34)

The steady-state surface coverage of the peroxide is given as:

KozCoz(0)bo, exp(-bo2902z)
T~O' Koz0 (0)bo, exp(- bo0,r02) + KH2 02bHzOz exp(- bH, O2rH202 j5-5

Expressions for Rt,H2 and ZD,Hz Were giVen by equations (5-22) and (5-23), respectively,
as defined in Model 1.

The impedance response for Model 2 can be expressed as the equivalent circuit shown

in Figure 5-2(a) for the anode and Figure 5-2(c) for the cathode. The boxes in Figures

5-2(a) represent a diffusion impedance corresponding to transport of hydrogen, and the
boxes in Figure 5-2(c) represent the Faradaic impedances corresponding to the proposed

reaction sequence. The term Z, in Figure 5-1 is given by


Ze = +(5-36)
(1
Zoz ZII2O,

It should be emphasized that Zo, is not the sum of Rt,o, and ZD,O, due to the surface

coverage. Similarly, ZHzOz cannot be considered to be a fre Iuener ~-i-'lllend.enden Rt,H2 02 -










[41] Y. Song, Y. Wei, H. Xu, M. Williams, Y. Liu, L. J. Bonville, H. R. K~unz, and J. M.
Fentona, I!1I' 11~.1..1 us~ !Il in high temperature proton exchange membrane fuel cells
cathode performance with ammonium carbonate," Journal of Power Sources, 141
(2005) 250-257.

[42] T. Ioroi and K(. Yasuda, "Platinum-Iridium Alloys as Oxygen Reduction Electro-
catalyss for Polymer Electrolyte Fuel Cells," Journal of the Electrochemical S -. .:. Iri,
152 (2005) Al917-Al924.

[43] J. R. C. Salgado, E. Antolini, and E. R. Gonzalez, "Pt-CoC Electrocatalys for
Oxygen Reduction in H2/02 [PEMFCs," Journal of the Electrochemical S -. .:. Iri,
(2004) A2143-A2149.

[44] P. J. Bouwman, W. Dmowski, J. Stanley, G. B. Cotton, and K(. E. Swider-Lyons,
"Platiunm-Iron Phosphate Electrocatalysts for Oxygen Reduction in PEMFCs,"
Journal of the Electrochemical S8... .:. Iri, 151 (2004) Al989-Al998.

[45] H. R. Colon-Mercado, H. K~im, and B. N. Popov, "Durability Study of Pt3Ni
Catalyst as Cathode in PEM Fuel Cells," Electrochemistry Communications, 6
(2004) 795-799.

[46] H. R. Colon-Mercado and B. N. Popov, "Stability of Pt Based Alloy Cathode
Catalysts in PEM Fuel Cells," Journal of Power Sources, 155 (2006) 253-263.

[47] T. Toda, H. Igarashi, H. Uchida, and M. Watanabe, "Enhancement of the elec-
troreduction of oxygen on Pt alloys witn Fe Ni Co," Journal of the Electrochemical
S8 .. .:. Iri, 146 (1999) 3750-3756.

[48] Y. Liu, A. Ishihara, S. Mitsushima, N. K ai- and K(. Ota, "Zirconia Oxide for
PEFC Cathode," Electrochemical Solid-State Letters, 8 (2005) A400-A402.

[49] A. Ishihara, K(. Lee, S. Doi, S. Mitsushima, N. M. Hara, K(. Domen, K(. Fukuda,
and K(. Ota, "Tantalum Oxynitride for Novel Cathode for PEFC," Electrochemical
Solid-State Letters, 8 (2005) A201-A203.

[50] A. H. C. Sirk, S. A. Campbell, and V. I. Birss, "Oxygen Reduction by Sol Derived
[Co, N, C,0]-Based Catalysts for use in Proton Exchange Membrane Fuel Cells,"
Electrochemical Solid-State Letters, 8 (2005) A104-A107.

[51] K(. Lee, A. Ishihara, S. Mitsushima, N. K~amiya, and K(. Ota, "Stability and Electro-
catalytic Activity for Oxygen Reduction in WC + Ta Catalyst," Electochimica Acta,
49 (2004) 3479-3485.

[52] G. Girishkumar, M. Rettker, R. Underhile, D. Binz, K(. Vinodgopal, P. McGinn,
and P. K~amat, "Singfle-Wall Carbon Nanotube-Based Proton Exchange Membrane
Assembly for Hydrogen Fuel Cells," Langmuir, 21 (2005) 8487-8494.
[53] K(. K~inoshita, Carbon~: EctohiclndP;.... /.;;..; Properties (Wiley: New
York, 1988).











10 1 .s ig 1V'11 .
o Real
a Imaginary
a Real
E Imaginary N
o on

10- C: B 10



0 100 200 300 400 0 100 200 300 400
Time /s Time /s
(a) (b)

Figure 7-8: The standard deviation of the single-frequency Impedance measurements
recorded at 0.4 A/cm2 and 70 oC as functions of time: a) at a frequency of 100 Hz; and b)
at a frequency of 1 Hz (as presented in Figure 7-7). The solid line represents the empirical
model developed for the error structure given by equation (7-1).


however, as shown in Figure 7-8(b), the standard devaitions for real and imaginary parts

are not equal at a frequency of 1 Hz. This result -II---- -R- that, even at a current density

of 0.4 A/cm2, Where the error structure was the smallest, some flooding may be taking

place.

Equation (7-1) provided a good representation of the impedance error structure

obtained at a current density of 0.4 A/cm2 under a broad variety of conditions. The error

structure for the impedance response collected at different temperatures is presented in

Figure 7-9(a) and the influence of anode/cathode back-pressure is explored in Figure

7-9(b). The model provided a good representation of the error structure for all cases

considered in Figure 7-9. Accordingly, equation (7-1) was used to represent the base-level

standard deviation for measurements unaffected by drying or flooding conditions.

7.2.2.3 Detection of flooded conditions

Impedance spectra were obtained at different current densities. The standard

deviations obtained at larger current densities are compared in Figure 7-10 to the values

obtained at 0.4 A/cm2. The standard deviations obtained for current densities of 1.0 and









iT = io2 + ipt;

na = (log((iT)./(Kh2. Ombulkh2). (1 (iT./ilimb2)))). /bh2;

VT = V (iT. Re ff) na;

y =[VT; iT; theta2];
w = -6 : .05 : 6; [Frequency range]

w =10.";

Ko02 = (w. + delta2)/do2;

bo2 = tanh(sgrt(i + Ko2))./(sgrt(i + Ko2));

Ci = 1./(RtH2 + ZDH2 + bh2);

Al = 1./(RtO2 + ZDO2 + bo2);

A2 = 1. g2./(RtO2 + ZDO2 + bo2);

B1 = 1. (1./RtPt f) + (1./RtPtb);

B2 = 1. ( f3 + f 4);

T = ((A2 + B2). (Al B1))./(2 + 96500 + i + 2 + 3.14 w B2 + A2 + f5);
z = re + (1./((A + Bl+ C1)+ T +(is 2 +3. 14 t w ~c))) + (1./((A1) +(i s 2 +3.14 t w ~c)));

zr = real (z);

zi = imag(z);










incorporate processes that may be responsible for the inductive response seen at low

frequencies. We found that side reactions producing hydrogen peroxide intermediates and

reactions causing Pt deactivation could vield inductive loops. These side reactions and the

intermediates can degrade fuel cell components such as nientranes and electrodes, thereby

reducing the lifetime the fuel cells. The hypothesized reaction involving of peroxide and

PtO formation were supported by microstructural characterization.

A more sensitive manner of using impedance spectroscopy to gain an insight into

the problem of flooding which adversely affects the performance of the fuel cell was

established. A comprehensive model for base-level noise in impedance measurements for

normal (non-flooded) conditions was developed and actual noise in flooded conditions was

calculated by transient fixed-frequency nicasurenients. A comparison of the actual noise to

the base-level noise was used to detect onset of floodingf.

Also, graphical methods were used to interpret impedance spectra in terms of

interfacial capacitance. The effective interfacial capacitance decreased with increase in

current and decreased slowly with time. The decreases in interfacial capacitance with

higher current density can he attributed to an excess amount of water i.e., flooding;

whereas, the decrease in interfacial capacitance with time may be related to catalyst

dissolution and deactivation.












- -- FC350


- -- FC350
n


3 N

10 1



O 01 C
10 I I I
103 10-2 101 100 101 102 103 103 102 101 100 101 102 103
flHz flHz

(a) (b)

Figure 4-4: Comparison of error structures for the FC350 (filled symbols) and the 850C.
The 0 represents the standard deviation of the real part of the impedance, and the a
represents the imaginary part of the impedance. The dashed and solid lines represents
the empirical model of the error structure given by equation 4-1. a) standard deviations
in units of impedance, and b) standard deviations normalized by the modulus of the
impedance.


where Rm is the current measuring resistor corresponding to a given current range and

a~, p, r, and 6 are constants determined for a given instrument and set of measurement

parameters. For the Gamry FC350, all adjusted parameters were equal to zero with the

exception of y = 0.679. For the Scribner 850C, all adjusted parameters were equal to zero

with the exception of a~ = 0.00213 and y = 0.679. Lines corresponding to equation (4-1)

are given in Figures 4-4(a) and 4-4(b). Equation (4-1) was used to weight subsequent

regressions to assess consistency with the K~ramers-K~ronig relations.

4.2.2 Evaluation of High-Frequency Bias Errors

In principle a complex fit of the measurement model could be used to assess the

consistency of impedance data. Sequential regression to either the real or the imaginary

parts was shown to provide greater sensitivity to lack of consistency.126 The measurement

model approach developed by Agarwal et al.126 WaS used to assess the consistency of

high-frequency data with the K~ramers-K~ronig relations. The Voigt model was fitted to the

real part of the measurement with a weighting based on the experimentally determined

stochastic error structure. The parameters so obtained were then used to predict the










CHAPTER 10
FUTURE DIRECTIONS

Recommendations for the future research of this work are presented in this chapter.

To gain better understanding into the proposed mechanisms, the following research plan

can be emploi-. I as a future direction of this project.

10.1 Parameter Evaluation

The experimental data can be regressed to the impedance models developed to

extract meaningful parameters such as rate constants for reaction kinetics, and transport

properties like diffusivity of species. Moreover, other information such as exchange current

density, and limiting current density can also be evaluated.

10.2 Ef~uent, and Microstructure Analysis

More work needed to provide evidence to support or disprove proposed reaction

mechanisms. ICP-MS can be applied to estimate platinum concentrations in the effluent

water of the fuel cell. IC (lon Chromatogratphy) can be used to estimate fluoride emission

rate in the effluent. The C'I. 11.111 4 I- Test K~it can be used to measure hydrogen peroxide

concentration,9 and the Orion Test K~it can be used to measure fluoride ion concentration

in the effluent water. The information found from the microstructural analysis and the

effluent an~ lli--; can be used to validate the proposition of the reaction mechanisms for

the model development, e.g., the platinum dissolution and the peroxide formation. The

fluoride ion concentration in the fuel cell effluent will give the information about lifetime

of the membrane.

10.3 One-Dimensional Flow Channel

The pseudo 1-Dimensional flow channel investigated should be 2.1, l1i-. I1 comprehen-

sively to improve the design further. Improved flow channel can be used to compare model

and experiment results in the search of kinetics and transport parameters important to

describe the fuel cell.










7-4 The standard deviation of the single-frequency Impedance measurements recorded
at 1.4 A/cm2 and 70 oC as functions of time: a) at a frequency of 100 Hz; and
b) at a frequency of 1 Hz (as presented in Figure 7-3). The solid line represents
the empirical model developed for the error structure given by equation (7-1). .127

7-5 The standard deviations for the real part of the impedance as a function of cur-
rnt density with frequency as a parameter for cell oeaina 0oC 2

7-6 Standard deviations for the impedance data obtained at a current density of
0.4 A/cm2. The solid line represents the empirical model developed for the er-
ror structure given by equation (7-1). The dashed lines represent the .I-i~lupl-
totic behavior of the model at high and low frequencies. .. .. .. 129

7-7 Impedance measurement recorded at 0.4 A/cm2 and 1 Hz as functions of time
at 70 oC: a) real part; and b) imaginary part. .... ... .. 130

7-8 The standard deviation of the single-frequency Impedance measurements recorded
at 0.4 A/cm2 and 70 oC as functions of time: a) at a frequency of 100 Hz; and
b) at a frequency of 1 Hz (as presented in Figure 7-7). The solid line represents
the empirical model developed for the error structure given by equation (7-1). .131

7-9 Standard deviations for the impedance data obtained at a current density of
0.4 A/cm2: a) With system temperature as a parameter; and b) at 70 oC with
anode/cathode back-pressure as a parameter. The solid line represents the em-
pirical model for the error structure given by equation (7-1). .. .. .. .. 132

7-10 Standard deviations for the impedance data obtained at a current densities of
0.4, 1.0, and 1.4 A/cm2. The solid line represents the empirical model for the
error structure given by equation (7-1). . .... .. 132

7-11 Normalized standard deviations for the real part of the impedance calculated
from the data shown in Figure 7-3 as a function of current density with frequency
as a parameter. ......... .. .. 133

7-12 The impedance data recorded using the MEA with a uniform GDL. The anode,
the cathode, and cell temperatures were set at 50 oC. ... .. .. 134

7-13 Normalized standard deviations for the real part of the impedance as a func-
tion of current density with frequency as a parameter for the MEA with a uni-
form pore distribution. The anode, the cathode, and cell temperatures were set
at 50 0C ... ......... .............. 135

7-14 Standard deviations for the impedance data obtained at a current densities of
0.02, 0.1, and 0.4 A/cm2. The solid line represents the empirical model for the
error structure given by equation (7-1). The anode, the cathode, and cell tem-
peratures were set at 70 oC. ......... .. .. 135



















T> memory of my late mother and .siblings

T> inspiration and .set .:; of my feather

T> dedication of my .sister-in-law



To say ;,.:I; Assaites. the best gift I heave received from GOD.










[15] D. Davies, P. Adcock, 31. Turpin, and S. Rowen, "Stainless Steel as Bipolar Plate
Material for Solid Polymer Fuel Cells," Journal of Power Sources, 86 (2000) 2:37-
242.

[16] H. van Bussel, F. K~oene, and R. Mallant, "Dynamic model of solid polymer fuel cell
water management," Journal of Power Sources, 71 (1998) 218-222.

[17] G. ?I1__;0.1, V. Recupero, and L. Pino, "Modeling PEM fuel cell: an innovative
approach," Journal of Power Sources, 101 (2001) 275-286.

[18] R. Roshandel, B. Farhanieha, and E. Saievar-Iranizad, "The Effects of Porosity
Distribution Variation on PEM Fuel Cell Performance," Renewable Energy, 30
(2005) 1557-1572.

[19] 31. Eikerling and A. A. K~ornyshev, "Electrochemical Impedance of the Cathode
Catalyst L ... ir in Polymer Electrolyte Fuel Cells," Journal of 1..~ I,~r..at.l;,..: a~l
C'i, in:i'.1, 475 (1999) 107-12:3.

[20] K(. T. Adjemian, S. J. Lee, S. Srinivasan, J. Benziger, and A. B. Bocarslya, "Silicon
Oxide Nafion Composite Membranes for Proton-Exchange Membrane Fuel Cell
Operation at 80-140C," Journal of the Electrochemical S. -- .:. Iri, 149 (2002) A256-
A261.

[21] C. Huang, K(. Tan, J. Lin, and K(. Tan, "XRD and XPS analysis of the degradation
of the polymer electrolyte in H2-02 fuel cell,," C'I, I,, Phys. Lett, 371 (200:3) 80-85.

[22] F. Liu, B. Yi, D. Xing, J. Yu, Z. Hou, and Y. Fu, "Development of novel self-
humidifying composite membranes for fuel cells," Journal of Power Sources, 124
(200:3)81-89.

[2:3] 31. Li, Z.-G. Shao, H. Zhang, Y. Zhang, X. Zhu, and B. Yi, "Self-Humidifying
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Membrane Fuel Cells," Electrochemical and Solid-State Letters, 9 (2006) A92-A95.

[24] M.-K(. Song, Y.-T. K~im, J. 31. Fenton, H. R. K~unz, and H.-W. Rhee, "C'I, am!! Illy-
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membrane fuel cells," Journal of Power Sources, 117 (200:3) 14-21.

[25] C. Heitner-Wirguin, "Recent Advances in Perfluorinated lonomer Membranes:
Structure, Properties and," J. M~embr. Sci., 120 (1996) 1-3:3.

[26] Y.-H. Liu, B. Yi, Z.-G.Shao, D. Xing, and H. Zhanga, "Carbon Nanotubes Rein-
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[27] 31. Doyle, S. Choi, and G. Proulx, "High-Temperature Proton Conducting Alem-
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Journal of the Electrochemical S. -- .:. I i, 147 (2000) :34-37.










3.2.2 Electrochemical Impedance Measurements

Impedance measurements were performed using two different systems. The Scribner

Associates 850C Fuel Cell Test Stand contains both an electronic load and a frequency

response analyzer. Impedance measurements obtained with the 850C were compared to

impedance collected using a Gamry Instruments FC350 impedance analyzer coupled with

a Dynaload electronic load RBL 100V-60A-400W. All electrochemical measurements were

performed with a two-electrode cell in which the anode was used as a pseudo-reference

electrode.

The protocol recommended by Ramani et al.192 WaS used to ensure that the system

reached steady-state operation before impedance measurements were taken. The protocol

consisted of two steps:

1. Upon startup, the current was swept from zero to the maximum value in forward

and reverse directions until hysteresis in the polarization curve was no longer

evident. This procedure was intended to ensure complete hydration of the MEA.

This step required up to 48 hours (break-in time) for a new MEA and 1.5 hours for

a system that had been recently used.

2. Once the hysteresis in the polarization curve was no longer evident, the current was

set and the potential was monitored. Impedance measurements were conducted after

the potential was stabilized. This step required 30 minutes.

The polarization curves were obtained by stepping the current from zero to the

maximum current with an increment of 10 mA/30 sec. A typical polarization curves is

presented in Figure 3-2.

Repeated impedance measurements were performed at several points on the polar-

ization curve. The impedance measurements were conducted in galavanostatic mode for

frequency range of 3 kHz to 1 mHz with a 10 mA peak-to-peak sinusoidal perturbation.

The corresponding potential perturbation ranged from 0.04 mV at high frequency to 0.4

mV at low frequency. The frequencies were spaced in logarithmic progression with 10





















a I


Figure 3-13: The configuration of the post flow channel.


problem of flooding in the interdigitated flow field though no experimental study has been

reported.

The performance of two conventional channels in term of polarization curves and

impedance spectra is presented in this section. In addition, a post flow channel design,

(shown in Figure 3-14) was proposed and performance of the new channel was compared

with the conventional channel. The polarization curves obtained for two channels from

steady-state measurement on the fuel cell is presented in Figure 3-14. The limiting

current obtained in the interdigfitated flow channel was about double of the current

obtained for the serpentine flow channel, which confirmed the interdigfitated channel

better performer. This observation was consistent with the reported literature.201,206 The

impedance response obtained for two channels in the fuel cell is presented in Figure 3-15.

The impedance spectra have general form consisted of one high-frequency capacitive

loop and one incomplete low-frequency inductive loop. The impedance in case of the

interdigfitated flow channel was found a lot less than the serpentine flow channel for same

operating conditions.

The performance of the post channel was compared with the interdigitated channel

for similar conditions. A comparison of polarization curves are presented in Figure 3-16.

As seen in this figure, the open-circuit potentials were comparable in both channels,

however, a reduced performance was noticed in both Ohmic and mass transfer regimes of










error analysis provides information that can he incorporated into regression of process

models.

The measurement model method for distinguishing between hias and stochastic errors

is based on using a generalized model as a filter for non-replicacy of impedance data. The

measurement model is composed of a superposition of line-shapes which can he arbitrarily

chosen subject to the constraint that the model satisfies the K~ramers-K~ronig relations.

The model composed of Voigft elements in series with a solution resistance, i.e..


Z = Ro + wrR (2-24)


has been shown to be a useful measurement model. With a sufficient number of parame-

ters, the Voigt model was able to provide a statistically significant fit to a broad variety of

impedance spectra.124

The measurement model is used first to filter lack of replication of repeated

impedance scans. The statistics of the residual errors yields an estimate for the variance

(or standard deviation) of stochastic measurement errors. This experimentally-determined

variance is then used to weight subsequent regression of the measurement model to deter-

mine consistency with the K~ramers-K~ronig relations. If the data can he represented by

a model that is itself consistent with the K~ramers-K~ronig relations, the data can he con-

sidered to be consistent. The concept of using a generalized measurement model to assess

consistency with the K~ramers-K~ronig relations, first introduced by Agarwal et al..124, 126, 131

was also emploi- II by Boukamp and 1\acdonaldl32 and by Boukamplas using weighting

strategies based on an assumed error structure. The experimental determination of the

stochastic error structure as used here, however, allows formal quantification of the extent

of agreement with the K~ramers-K~ronig relations.

Other transfer-function models can he used as a measurement model so long as they

are consistent with the K~ramers-K~ronigf relations. Shukla and Orazem have demonstrated

that the stochastic error structure determined from replicated impedance measurements is










3-17 Impedance response of the new flow channel with 850C for H2 aS TreCtREL at
the anode and air as oxidant at cathode. The anode and the cell temperatures
were set at 50 oC and the cathode temperature at 45 oC. The fuel cell was as-
sembled with a uniform porous GDL; a) impedance response generated for the
new channel as a function of current density; and b) impedance response recorded
at 0.4 A/cm2 for the two channels. . ...... .. 73

4-1 Polarization curve generated from the steady-state measurement with 850C for
H2 aS reactant at the anode and air as oxidant at cathode. The anode reactant
stream and cell temperatures were set at 40 oC and the cathode reactant stream
temperature at 35 oC. ......... . .. 75

4-2 The average time required for impedance measurement at each frequency. The
error bars associated with the standard deviation obtained from four experi-
ments is smaller than the symbols used in the figure. ... .. .. 76

4-3 Five scans of impedance data collected at a current density of 0.2 A/cm2 With
the FC350. ......... ... .. 77

4-4 Comparison of error structures for the FC350 (filled symbols) and the 850C.
The 0 represents the standard deviation of the real part of the impedance, and
the a represents the imaginary part of the impedance. The dashed and solid
lines represents the empirical model of the error structure given by equation
4-1. a) standard deviations in units of impedance; and b) standard deviations
normalized by the modulus of the impedance. .... ... .. 78

4-5 Regression of the Voigt model to the real part of the impedance correspond-
ing to the second of five scans given in Figure 4-3: a) fit to the real part of the
measurement; and b) prediction of the imaginary part. The 0 represents the ex-
perimental data, the heavy solid line represents the measurement model fit, and
the thin solid lines represent confidence intervals. ... ... .. 79

4-6 Normalized residual errors for the regression presented in Figure 4-5: a) fit to
the real part, where dashed lines represent the +2o- bound for the stochastic
error; and b) prediction of the imaginary part, where solid lines represent the
95. !' confidence intervals for the model obtained by Monte Carlo simulations. 80

4-7 Detailed representation of impedance data showing the inconsistency observed
at high frequency: a) expanded view of Figure 4-5(b); b) expanded view of a
Nyquist representation (see Figure 4-3 for a complete spectrum). The filled sym-
bols correspond to data that were deemed inconsistent with the K~ramers-K~ronigf
relations. ......... . ... . 81

4-8 Regression of the Voigt model to the imaginary part of the impedance corre-
sponding to the first of five scans given in Figure 4-3: a) fit to the imaginary
part of the measurement; and b) prediction of the real part. The 0 represents
the experimental data, the heavy solid line represents the measurement model
fit, and the thin solid lines represent confidence intervals. .. .. .. 82












0.8 o 0.8 Hydrogen Peroxide
8 ydroen eroxde Platinum Oxide
o Platinum Oxide > 0.6-
0.6 o
S0.4 -0 0.




(a) (b
Figure~~~~~~~~~ 5-5 rcinlsrfc-oeaeo h itreitspotd )a ucino


cell p potential and b)ren asnt aA fucin fcrrneniy





Several authors have proposed that the low-frequency inductive loops could be

attributed to relaxation of adsorbed intermediates species associated with cathodic

reactions.208, 144,209 The present work shows that cathodic reactions involving formation

of peroxide intermediates and reactions involving formation of PtO and subsequent

dissolution of platinum can result in low-frequency inductive loops. An interesting aspect

of Model 3 is that the inductive loop is controlled by formation of PtO. The corresponding

low-frequency inductive loops can be seen even at very low rates of Pt dissolution. These

interpretations are supported by a growing number of articles in the recent literature

describing evidence of peroxide formation and platinum dissolution under normal PEM

operating conditions.87, 96-98, 93, 90, 99

Models based on proposed reaction hypothesis can be used to gain insight into the

reaction mechanism. For example, Models 2 and 3, respectively, invoked surface coverage

by peroxide and PtO. The surface coverage predicted by these models is presented in

Figures 5-15(a) and 5-15(b) as function of potential and current density, respectively. As

shown in Figure 5-15(a), the fractional coverage of the intermediates in both the models

increased with the increase in the cell potential. The presentation in Figure 5-15(b) as










[79] J. Jiang and A. K~ucernak, Il~i.; -I i, II .1.4 of fuel cell reactions at the composite
microelectrode solid polymer electrolyte interface I. hydrogen oxidation at the
nanostructure Pt-Nafion membrane interface," ora f. t.tai.-Cou.-r
567 (2004) 12:31:37.

[80] V. Stemeankovic, B.N.Gurgur, P.N.Ross, and M.N.Markovic, "Oxygen Reduction
Reaction on Pt and Pt-Bimetallic Electrodes Covered with CO, mechanism of
air bleed effect of reformate," Journal of the Electrochemical S. -- .:. Iri, 152 (2005)
A277-A282.

[81] V. A. Sethuraman, J. W. Weidner, A. T. Haug, S.Motupally, and L. V. Protsailo,
"Hydrogen Peroxide Formation Rates in a PEMFC Anode and Cathode Effect of
Humidity and Temperature," Journal of the Electrochemical S8... .:. Iri, 155 (2008)
B50-B57.

[82] A. Ohma, S. Suga, S. Yamamoto, and K(.Shinohara, il, 11.1.1 .Il.- Degradation
Behavior during Open-Circuit Voltage Hold Test," (2007).

[8:3] A. B. Laconti, 31. Alamdan, and R. C. MacDonald, Handbook of Fuel C'ell~s, vol-
ume :3, 2nd edition (New York: John Wiley and Sons, 200:3).

[84] E. Endoh, S. Terazono, B.Widli ii I and Y. Takimoto, "Degradation Study of MEA
for PEMFCs under Low Humidity Conditions," Electrochemical and Solid-State
Letters, 7 (2004) A209-A211.

[85] 31. Inaba, "Degradation Mechanism of Polymer Electrolyte Fuel Cells," in 14th
International C'onference on Properties of Water and Stesam in Kyoto. (2004)
:395-402.

[86] X. Huang, R. Solasi, Y. Zou, 31. Feshler, K(. Reifsnider, D. Condit, S. Burlastsky,
and T. Madden, i l. I I! .1... d1 Endurance of Polymer Electrolyte Membrane and
PEM Fuel Cell Durability," Journal of Polymer Science: Part B: Polymer Ph ;;i ..
44 (2006) 2:346-2357.

[87] J. Qiao, 31. Saito, K(. H1- .; ...1 ii and T. Okada, "Degfradation of Perfluorinated
lonomer Membranes for PEMFuel Cells during Processing with H202," Journal of
the Electrochemical S -. .. l~i, 153 (2006) A967-A974.

[88] T. Patterson, "Fuel Cell Technology Topical Conference Proceedings," in Fuel C'ell
T. In... J..,i;; Topical C'onference Proceedings, AIChE Spring National Meeting (2002)
2:35.

[89] 31. Cai, 31. S. Ruthkosky, B. Merzougui, S. Swalhl~it Im 31. P. Balogh, and S. H.
Oha, Il~i.; -I i, 1I .~ of thermal and electrochemical degradation of fuel cell cata-
lysts," Journal of Power Sources, 160 (2006) 977-986.

[90] H. Xu, R. K~unz, and J. 31. Fenton, l~ie.- -I ay, .I n. I. of Platinum Oxidation in PEM
Fuel Cells at Various Relative Humidities," Electrochemical and Solid-State Letters,
10 (2007) B1B5.
























1.05--
-o- Fresh MEA
0.90 --n- Used for 500 h
0.75-


0.60-
141

i~0.30 -


S0.15 -


1 11 11 .
0.0 0.1 0.2 0.3 0.4 0.5

Current Density / A cm-2

Figure 6-6: Polarization curve generated from the steady-state measurement for different
time with 850C for H2 as reactant at the anode and air as oxidant at cathode. The anode
reactant stream and cell temperatures were set at 40 oC and the cathode reactant stream
temperature at 35 oC. The fuel cell was assembled with a serpentine flow channel, and a
uniform porous GDL.









6.2.4.2 Transmission electron microscope

The TEM study was performed with a JOEL JSM-2010F Field Emission Electron

Microscope available at MAIC in the University of Florida, which is equipped with an

energy dispersive spectrometer (EDS) for compositional analysis. The TEM micrographs

were taken at 200 kV accelerating voltage for several magfnifications in bright field

mode (transmitted electrons). Samples were prepared following procedure reported

in literature.193 A small portion from the center of the both fresh and used MEA was

cut with sharp razor and was embedded on epoxy resin (Araldite 5002) for 48 hours at

600C. Thin (90 nm) sections from the membrane-electrodes interfaces were cut with a

diamond knife on Reichert OMU3 ultramicrotome at room temperature. The samples were

mounted on Cu grid (mesh size 200) prior to TEM study.

6.2.4.3 X-ray photoelectron spectroscopy

The XPS was used to inspect possible elements and compounds at the surface

(5-15 atomic 1 u. ris) of the MEA. For sample preparation, a small portion from the

center of the both fresh and used MEA was cut with sharp razor and the XPS scans

were taken with the PHI 5100 ESCA system by Perkin-Elmer available at MAIC in the

University of Florida. X-ray source was Mg anode with a work function 4.8 eV. The

emitted electrons were collected at 45 o with respect to the sample. The sample was

scanned at 300 watts power in energy range of 1000-0 eV (binding energy) with a step of

0.5 eV and 30 mSec/step. The survey (full scan) was generated at pass energy 89.45 eV

whereas narrow scans (high resolution) for several peaks were performed at pass energy

of 22.36 eV. The atoms were assigned according to binding energy of visible peaks and

atomic composition of elements were evaluated by relatives intensities of the peaks.

6.3 Results

The results obtained from the surface analysis of the cathode surface, and supporting

observation obtained from electrochemical response, and effluent analysis are presented in

this section.











2.5 --
100
2.0 -Total Current Total Current
-Equation (26) 10' t *Equation (43)
15- -Equation (27) <( -- -Equation (39)


1.0 --1 -


0.5 10-4

0.0 I I I I I 105
0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0
Potential /V Potential /V

(a) (b)


Figure 5-8: Relative contributions of two reactions to total current at the cathode: a)
Model 2; and b) Model :3.



0.50- .-o


S0.25 -O Experimental data
C: Model 2
-Model 3
N
0.00

0.00 0.25 0.50 0.75 1.00 1.25 1.50
Z / cm2


Figure 5-9: Impedance response for 0.05 A/cm2 generated by Models 2 and :3 for 40 oC us-
ing parameters reported in Table 5-1 and compared with the experimental data presented
in Figure 5-:3(b).


loop. A comparison between the model and experiment is presented in Nyquist-format

in Figure 5-9 for current densities in the kinetically controlled part of the polarization

curve. The real and imaginary parts of the impedance are presented as functions of

frequency in Figures 5-10(a) and 5-10(b), respectively. Similar results are shown in

Figures 5-11, 5-12(a), and 5-12(b) for the intermediate current density and in Figures

5-13, 5-14(a), and 5-14(b) for high current densities. Impedance measurements are much

more sensitive than polarization curves to the presence of minor reactions. Both Models 2










[202] A. Su, Y. C. Chiu, and F. B. W ng_ "The Impact of Flow Field Pattern on Concen-
tration ~ ~ ~ III an eromnc nPEF, International Journal of Energy Research, 29
(2005) 409-425.

[203] Y. Yoon, W. Lee, G. Park, T. Yang, and C. K~im, "Effects of C'I I1.11. I Configurations
of Flo Field Plte onI th Perormnc ofI aII PEMFC,"II~ I ~I II Electochimica Acta, 50
(2004) 709-712.

[204] S. Dutta, S. Shimpalee, and J. W. V. Zee, "Three-Dimensional Numerical Simula-
tion of Straight C'I .Ill., I PEM Fuel Cell," Journal of Applied Electrochemistry, 30
(2000) 135-146.

[205] W. k. Lee, S. Shimpalee, and J. W. V. Zee, "Verifying Predictions of Water and
Current Distributions in a Serpentine Flow Field Polymer Electrolyte Membrane,"
Journal of The Electrochemical S8... .:. Iri, 150 (2005) A341-A348.

[206] A. K~azim, H. T. Liu, and P. Forges, "Modeling of Performance of PEM Fuel Cells
with Conventional and Interdigitated Flow Fields," Journal of Applied Electrochem-
istry, 29 (1999) 1409-1416.

[207] T. V. Nguyen, "A Gas Distributor Design for Proton-Exchange-Membrane Fuel
Cells," Journal of the Electrochemical S -- .:. Iri, 143 (1996) L103.

[208] R. Makharia, M. F. Mathias, and D. R. Baker, \!. I-llrement of Cl Iif s-( L i-; r
Electrolyte Resistance in PEFCs using Electrochemical Impedance Spectroscopy,
Journal of the Electrochemical So .:. I r, 152 (2005) A970-A977.

[209] Y. Bultel, L. Genies, O. Antoine, P. Ozil, and R. Durand, "Modeling Impedance
Diagrams of Active L ... r-s in Gas Diffusion Electrodes: Diffusion, Ohmic Drop
Effects and Multistep Reactions," Journal of Elects r -at..ali..a l Clo, I,,.I ry, 527
(2002) 143-155.

[210] M. E. Orazem, T. E. Moustafid, C. Deslouis, and B. Tribollet, "The Error Structure
of Impedance Spectroscopy Measurements for Systems with a Large Ohmic Resis-
tance with Respect to the Polarization Impedance," Journal of the Electrochemical
S8 .. .:. Iri, 143 (1996) 3880-3890.

[211] S. K(. Roy and M. E. Orazem, "Use of Deterministic Impedance Models for Inter-
pretation of Low-Fr-equency Inductive Loops in PEM Fuel Cells," ECST-Proton
El. I,;r,:.l.- Membrane Fuel Cells 6, 3 (2006) 1031-1040.

[212] I. Epelboin, M. K~eddam, and J. C. Lestrade, I I) III i o: impedance and intermedi-
ates in electrochemical reactions," Drt.1.ttil Discussions, 56 (1975) 264-275.

[213] R. D. Armastron, R. E. Firman, and H. R. Thirsk, "AC Impedance of complex
eeletrochemical reactions," Dr,~r.1.tti Discussions, 56 (1975) 244-263.

[214] R. D. Armstrong and K(. Edmondson, "The impedance of metals in the passive and
transpassive regions," Electochimica Acta, 18 (1973) 937-943.









5.4.3 Model 3: Platinum Dissolution

The platinum dissolution was assumed to occur by a reaction scheme similar to that

reported by Darling et al.,1o i.e., by an electrochemical reaction


Pt + H20 0 PtO + 2H+ + 2e- (5-37)


in which PtO is formed, followed by a chemical dissolution reaction


PtO + 2H+ Pt+2 + H20 (5-38)


The model developed by Darling and M.~ i-- r-s resulted in an equilibrium oxide coverage

by PtO.1o A similar reaction scheme for Pt dissolution with PtO as an intermediate at

the cathodic potential of the fuel cell has also been reported by Dam et al.91 Also, Xu et

al.215 have reported two schemes for Pt oxidation at the cathode, both having PtO as an

intermediate.

The current density corresponding to reaction (5-37) was given by


ipt = Kpt,f(1 7Pto) exp (bpt,frlPt, f) KPt,bYPtO exp (-bPt,brlPt,b) (5-39)


where Kpt,f = nF~kptf,, KPt,b = nFkPt~b, a = 2, P is the maximum surface coverage, and

7PtO is the fractional surface coverage by PtO. The dissolution of PtO was assumed to

occur according to

TPtO = K3YPtO (5-40)

and the corresponding material balance for the PtO was expressed as

dYPtO iPt
0 -reto (5-41)
dt 2F

The formation of the platinum oxide was proposed to have an indirect influence on

the ORR at the cathode by changing the effective rate constant for the reaction. Thus,


Keff = Kpt + (KPto KPt)7PtO (5-42)
















































with increasing current density, an effect which was -II__- -rh I1 in the literaturel2,157 to be

due partially to flooding. The impedance spectra were relatively smooth for low current

densities, however, the spectra have significant scatter at higher current densities where

flooding was probable. The scatter was particularly evident at low frequency, where

the spectra show jumps in value which may be associated with removal of condensed

water. Similar results were observed at other temperatures. The impedance measured

at 70 oC is presented in Figure 7-2 with current density as a parameter. Here also the

impedance data have greater degree of scatter at higher current densities, and this scatter

is particularly evident at lower frequencies.


40 Hz
sca~o 0 00 0 0 0.4 A cm-2



1 k 00
O 0.01 kHz

00 0.10 0.20 0.30 0.40 0.50
Z / cm2


40 Hz
Ogo OOOODO1.4Acm-2




1"" 0.01 0Hz
s l ll e l l


Figure 7-1: Impedance data recorded with the 850C with applied current
parameter. The anode, cathode, and cell temperatures were set to 50 oC.


ed


ed


:nsity as a

















Insity as a


N
E
o
c:
N


0.30

Z / cm2


Figure 7-2: Impedance data recorded with the 850C with applied current
parameter. The anode, cathode, and cell temperatures were set to 70 oC.




















GAS DIFFUSION BACK(ING


Figure 2-4: A schematic representation of membrane electrode assembly(\ll- A)(taken from
literature)


required platinum loading (generally less than 0.5mg Pt/cm2). The Pt/C powder is mixed

with small quantity of the Nafion electrolyte to ensure proton conduction. In practice,

the thickness of the catalyst 1.,-c c is between 10-50 micron. While a thin 1.,-c c is preferred

for better reactants diffusion and catalyst utilization, a thick 1.,-c c incorporates higher

catalyst loading thus catalyst 1 .,-cv optimization requires a delicate balance between

mass transport and catalytic activity concerns. To distribute Pt on Carbon uniformly, a

surfactant is -II_t---- -1.. which stabilizes the nanoparticles of Pt and prevent .I__-oegfation.40

Also, use of an optimum amount of ammonium carbonate as an additive to catalyst 1.,-< c

is -II_t---- -1.. which aids in pore forming thus improves the mass-transport limitations.41

To reduce the cost of cathode catalyst, alloys such as Platinum-Iridium (Pt Ir ,42

Pt-Cobalt (Pt Co),4:3 Pt-Iron Phosphate (Pt FeP(4)444 have been investigated as

possible cathode materials. The problem with these transition metal alloys are durability,

these are unstable in acidic environment of the fuel cell. Addition of Ni in Pt-alloy

(Pt:3Ni), was observed to shorten the Pt-Pt interatomic distance, thus resulting in

stronger handing reducing dissolution and loss of catalyst. However, the alloy shows

higher interfacial resistance, and dissolution of metal in fuel cell environment, and

subsequent diffusion of Ni into membrane can degrade the lifetime of fuel cell.45 Similarly,

less expensive catalysts by alloying Pt with Fe Ni Co were explored; the initial
















PEM Fuel Cells
Electron Flowu
Load


bipolar
plate

gas diffusiorn f
layer electrode


Membrane


(b)

Figure 2-1: Illustration of the fuel cell (taken from literaturel; a) flow diagram; and b)
components.


OI water










6-1 Full-scan XPS spectrum of the used sample generated at pass energy 89.45 eV.
XPS scans were taken with the PHI 5100 ESCA system by Perkin-Elmer avail-
able at MAIC in the University of Florida. X-ray source was Mg anode with a
work function 4.8 eV. The sample was scanned at :300 watts power in energy
range of 1000-0 eV findingg energy) with a step of 0.5 eV and :30 n1Sec/step. .118

6-2 High resolution performed at pass energy of 22.36 eV of the XPS spectra on
Pt peaks. XPS scans were taken with the PHI 5100 ESCA system by Perkin-
Elmer available at MAIC in the University of Florida. X-ray source was Mg an-
ode with a work function 4.8 eV. The sample was scanned at :300 watts power
in energy range of 1000-0 eV findingg energy) with a step of 0.5 eV and :30 n1Sec/step. 119

6-3 TEM images of cathode surfaces. TEM study was performed with a JOEL JSM-
2010F Field Emission Electron Microscope available at MAIC in the University
of Florida. The TEM micrographs of cathode surfaces were taken at 200 kV ac-
celerating voltage in bright field mode; a) fresh sample; and b) used sample. 119

6-4 TEM images of cross-section. TEM study was performed with a JOEL JSM-
2010F Field Emission Electron Microscope available at MAIC in the University
of Florida. The TEM micrographs were taken at 200 kV accelerating voltage in
bright field mode;; a) fresh sample; and b) used sample. .. .. .. 120

6-5 SENT micrographs of cathode cross-section were taken at 15 kV accelerating volt-
age. The cross-section of the both fresh and used MEA was cut with sharp ra-
zor and the samples were coated with Au-Pd; a) fresh sample; and b) used sant-
ple............... ............... 121

6-6 Polarization curve generated front the steady-state measurement for different
time with 850C for H2 as reactant at the anode and air as oxidant at cathode.
The anode reactant stream and cell temperatures were set at 40 oC and the cath-
ode reactant stream temperature at :35 oC. The fuel cell was assembled with a
serpentine flow channel, and a uniform porous GDL. ... .. . .. 122

6-7 Impedance responses collected at at 0.2 A/cH72 Rs a function Of tines a func-
tion of time with 850C for a function of time for H2 as reactant at the anode
and air as oxidant at cathode. The anode and the cell temperatures were set at
40 oC and the cathode temperature at :35 oC. The fuel cell was assembled with
a serpentine flow channel, and a uniform porous GDL. .. .. .. 12:3

7-1 Impedance data recorded with the 850C with applied current density as a pa-
ranleter. The anode, cathode, and cell temperatures were set to 50 oC. .. .. 125

7-2 Impedance data recorded with the 850C with applied current density as a pa-
ranleter. The anode, cathode, and cell temperatures were set to 70 oC. .. .. 125

7-:3 Single-frequency Impedance measurements recorded at 0.1 Hz, 70 oC, and 1.4
A/eni2 Rs functiOUs Of time: a) real part; and b) imaginary part. .. .. .. .. 126













-030 p o E 0 30b psi oaa

000a kz01 z05 1H
-0 05 02 ; 04 306 08t 100 0 02 0 6 0 0 2 1 6 1
Z / 0 cm2 Z / 30 cm26a
-o(oa) (b)t1~bc-3 d o4 s
Fiur 3-:Cl efrmnea ucto fbcpesue h esreet eecn
dutdwt 5C o 2R ecan tteaoean i soiat tctoe h
anoe racantsteamandcel tmpratre wee st t 6 o an th cthoe eacan


A/cm2m





tigranpr of7 reacans.9 Howornever a ntio hihe backpressure. the performance would con-
trolled by electrode kinetis resulting in thnod enhancement of ian cel pefrance. Inadtion

ao reactant crssoveruc asd ofl hydroen ars beenreporte at enhOCancd bh ackpressre,197n

which an tpreduce th performance of te cell.wsasmldwt sretn hne;a
3.3.4 c Hytresiose Behavior and. I/mpedance Resnpln~ ponsepr~rlpl a


Galvanodynami cunenrves wreact measured inforwade andc revers directios The for-

ward andrever sea direction ofa theno resuling hytergesi curves are deined in the lieteratr

tasotob the weaterimibti~ on adter wat hger-draiacyles, restepetively.19 Aol hysersi


crveatn crsobtained at 0o ofo a scan rate of e 50 ore mA/3 sspeentaned in Figre 3-8a). n th



hysteresis mi curve, the esuedi forward and backardsca directions weentdsigihabe for-





higher current densities due to multiple crossing of water-imbibition and water-drainage

cycles. The multiple crossing of the two cycles could be attributed to random movement of

water-droplets, which characterizes floodingf to be a stochastic process. A zoomed picture

of the flooding region (high current density) is shown in Figure 3-8(b).










capacitance is usually scaled to electrochemical active surface area of catalyst.22 A

decrease in effective surface area of roughly 60 percent was found under drying conditions,

and a decrease of roughly was found under flooding conditions.

The higher value estimated for the interfacial capacitance could contribute to the

improved performances of the fuel cell at elevated temperature and elevated operating

pressure.196 The sensitivity of interfacial capacitance to poor water management accounts

for the small values of capacitance when using a uniform GDL. The capacitance was

larger when using a micro-macro porous GDL, which is reported to provide better water

management.64-66 The sharp decrease in Ceaf at low current densities observed for the

non-uniform GDL is likely due to drying of the membrane.152, 12 Similar experiments were

not performed for the uniform GDL. The observation of a higher value of the interfacial

capacitance for the interdigfitated flow channel is consistent with observation of higher

current densities and better fuel cell performance as compared to the serpentine flow

channel.4, 200,206,207 A moderate decrease in the value of Ceaf with time was observed.

The observed decrease in the interfacial capacitance can be converted into an equivalent

decrease in the electrochemical active surface area with time, which could be due to the

slow approach to steady-state operation.194










ketone)s, poly(arylene ether sulfome)s, polyhenzimidazoles, etc. Advantages of using these

materials are lower cost than perfluorinated membranes, inclusion of polar groups to

improve water uptake over a range of temperatures, and the possibility of recycling by

conventional methods.

The six-membered ring of the naphthalenic polyimide is much more stable to hydrol-

ysis, this membrane is better suited for fuel cell applications"" while five-membered ring

polyimides which may undergo hydrolysis of the phthalimide structure under strong acid

conditions quickly leads to chain scission and causes the membrane to become brittle.3

This indicates that the stability of the highly cross-linked membranes is not only caused

by cross-linking of the pclh-r i-1. to chains, which slows down the loss of -SOHH from the

membranes, but also by reduced gas crossover and, therefore, reduced HO2* and OH- for-

mation. High degrees of cross-linking (more than 12) could improve the stability, however,

the simultaneous increase of membrane resistance might not he tolerable. The optimum

membrane thickness, which, as a compromise between gas crossover and resistance, must

he found. Another crucial point is the C O C bond breaking, initiated by attack of

OH-. In the presence of both OH- radicals and oxygen, complete degradation of the

aromatic rings can he achieved within a few hours. In view of this, the saturated and

perfluorinated Nafion which is much more inert has an inherent advantage over the new

membranes based on aromatic hydrocarbons.

2.2.2 Electrodes

The major requirements for an effective catalyst are high activity, high electrical con-

ductivity, high proton conductivity, low corrosion, high porosity, high mechanical strength,

and highly porous to ensure good gas access. State-of-the-art catalysts utilize nano-sized

platinum particles (3-10 nm) supported on a high surface area carbon powder (30-50

nm). While platinum provides the catalytic activity, the carbon provides the electrical

conductivity necessary to harvest electrons to/from the active sites. The carbon-supported

platinum (Pt/C) structure offers a high catalytic surface area, significantly reducing the












:3.3.1 Current Density as a Parameter ..... ... .. 61
:3.3.2 Temperature as a Parameter ...... .... .. 62
:3.3.3 Backpressure as a Parameter ...... .... .. 62
:3.3.4 Hysteresis Behavior and Impedance Response .. .. .. 65
:3.3.5 Time as a Parameter ........ ... .. 66
:3.3.6 Flow C'I I1.11. I as a Parameter ...... .. . 69

4 ERROR ANALYSIS OF IMPEDANCE RESPONSE ... .. .. 74

4.1 Introduction ......... . .. .. 74
4.2 Results. ............ ......... 76
4.2.1 Evaluation of Stochastic Errors ..... ... .. 76
4.2.2 Evaluation of High-Frequency Bias Errors .. .. .. .. 78
4.2.3 Evaluation of Low-Frequency Bias Errors .. .. .. .. 82
4.2.4 Impedance Response after Error Analysis .. .. .. .. 85
4.3 Discussion ......... . .. 87

5 INTERPRETATION OF IMPEDANCE RESPONSE .. .. .. .. 89

5.1 Introduction ......... . .. 89
5.2 Class of Model Development ....... ... .. 89
5.3 Model Framework ......... . .. 90
5.3.1 Polarization Curve ......... ... .. 90
5.3.2 Impedance Response . ..... ... .. 91
5.4 Impedance Response for Proposed Reaction Mechanisms .. .. .. .. 92
5.4.1 Model 1: Simple Reaction K~inetics .... .. .. 9:3
5.4.2 Model 2: Hydrogen Peroxide Formation ... .. .. .. 95
5.4.3 Model :3: Platinum Dissolution ..... .. . 99
5.5 Results. ........ .. .... ......... 101
5.5.1 Experimental Polarization and Impedance Results .. .. .. .. 102
5.5.2 Model Response Analysis . ..... .. .. 102
5.5.2.1 Model 1 . ..... ... .. 104
5.5.2.2 Models 2 and :3 . ..... .. .. 106
5.6 Discussion ......... . .. 110

6 RESITLTS OF EX-SITIT ANALYSIS . ...... .. .. 11:3

6.1 Introduction . .... .... .. .1:3
6.2 Experimental . ..... ...... .14
6.2.1 Materials and Chemicals . ..... .. .. 114
6.2.2 Electrochentical Impedance Measurements .. .. . .. 115
6.2.3 Aging Protocol for the Samples ..... ... .. 115
6.2.4 Surface Analysis ......... .. .. 115
6.2.4.1 Scanning electron microscope ... .. .. 115
6.2.4.2 Transmission electron microscope ... .. .. .. 116
6.2.4.3 X-ray photoelectron spectroscopy .. .. . .. 116
6.3 Results ......... ... .. 116










cathodic potential. While their work supports formation of peroxide at the cathode of

the fuel cell, peroxide formation at the anode is also possible due to 02 CTOSSOVer. A more

inclusive impedance model could be developed by accounting for peroxide formation at the

anode.

The steady-state current for reaction (5-24) can be expressed as


io, = -Kozco,(0) (1 YH2O,) exp (-bo, r0,) (5-26)


where Ko, = nFko, with the same notation defined for Model 1, a = 2, and yH202 iS the

fractional surface coverage of hydrogen peroxide. The current density corresponding to the

reaction (5-25) can be expressed as


iHzOz = -KH2O,7H2O, exp (-bHzOzrlHzOz) (5-27)


where KHz02 = nF~kH202, a = 2, and 0 is the maximum surface coverage. The

electrochemical reaction at the anode was given as reaction (5-17), and the corresponding

current expression was given as equation (5-18). Diffusion of peroxide away from the

catalyst surface was ignored in the present work. Thus, the peroxide produced by reaction

(5-24) was subsequently consumed in reaction (5-25) to form water.

The overall impedance was calculated as

1 1
Z = Re + + (5-28)
Rt,H2 ZD,H2 e j2rFFw-B 0

where
1 1
Zea = +~ (5-29)
Rt,o, + ZD,O, Rt,H2O,
1 1 1 1 50
(Rtoo, + D0) HO) t,H202YH20, [ t,02 ZD,02 Rt,Hz02
and
1 1
(Rtgo, + ZD~,O) 1 yHgO,) Rt,HO202H20O,31










This loss mainly arises from the mass-transport resistance in catalyst and diffusion

lI-;-ir However, mass-transport in the diffusion 1... -r can also be affected by the channel

geometry of the flow field plate. In addition, at high current density hefty amounts

of water are produced, which causes flooding of the cathode surface and inhibits the

transport of reactants as well as ionic species.

The physical properties of the diffusion 111-;- rs such as porosity can be affected by

several factors, which may result into mass-transport overpotential. At high current

densities, the porosity is reduced compared to the dry state by the presence of liquid

water. The porosity of the diffusion 1 ... r~s is also affected by the compression force applied

while assembling the fuel cell. Excessive compression reduces the porosity which hinders

gas-transport, whereas too little compression may cause an increase in contact resistances.

The mass-transport loss at very high current densities is also attributed to drying of the

anode.16

2.1.4 Parasitic Potential Loss

Even in the limit of zero current in the fuel cell, the output voltage of the cell is less

than the thermodynamically predicted voltage. This decrease is due to gas crossover and

undesired electron leaks across the electrolyte membrane. Fuel crossover is the amount

of fuel that crosses the membrane from the anode to the cathode without being oxidized

at the anode catalyst 1 ... r, which results in a loss of fuel. Internal current is the flow of

electron from the anode to the cathode through the membrane instead of going through

the external circuit. Many other unknown processes can also contribute to this loss, one of

the processes can be proton transport thorough the membrane which defined as convection

overpotential given as:171

rlconv. = FVCH+ m4 (2-9)

where CH+ is proton concentration, v is water velocity in the membrane, Im is thickness of

membrane, and k is membrane conductivity.









electron exchanged in the reaction. The steady-state surface coverage was calculated by

material balance of the intermediates involved in the proposed reaction mechanism.

The steady-state current for each reaction was calculated as function of overpotential

using the values of the steady-state surface coverage and concentrations. The total

steady-state current was calculated by adding current contributions from all participating

reactions at the cathode, and the total current at the anode was equated to the total

current from the cathode to calculate the anode overpotential rla, i.e.,


Go=1 logT,c 54
r bH2 KHCHOO (5 -


where ir,c is the total cathode current, KH, iS the rate constant for the HOR defined as in

equation (5-18), cH, iS the concentration of the hydrogen, and bH, iS the Tafel constant for

the HOR. The cell potential U was given by


U = Ueq. rlc (- Ga) IRe (5-5)


where rle is the cathode overpotential and Re is the frequena i~~l-independent ohmic resis-

tance.

5.3.2 Impedance Response

The Faradaic current density can be expressed in terms of a steady state contribution

i and an oscillating contribution i as


if= l Re py exp (jut) (5-6)

where j = 2/-, t is time, and w is the frequency in units of s l. A Taylor series

expansion of equation (5-1) about the steady-state value yields

8f 8f 8f
if = VIi0,r V + cs ~ Y C(0) + ]k (5-7)


where V ,ci(0) and ~kr Were aSSumed to have small magnitudes such that the higher-order

terms in the expansion can be neglected.










[164] J. R. Macdonald, "Frequency Response of Unified Dielectric and Conductive
Systems Involving an Exponential Distribution of Activation Energies," Journal of
Applied Ph;,:. -, 58 (1985) 1955-1970.

[165] R. L. Hurt and J. R. Macdonald, "Distributed Circuit Elements in Impedance
Spectroscopy: A Unified Treatment of Conductive and Dielectric Systems," Solid
State lonics, 20 (1986) 111-124.

[166] J. R. Macdonald, "Linear Relaxation: Distributions, Thermal Activation, Structure,
and Ambiguity," Journal of Applied Ph ;,;: ;, 62 (1987) R51-R62.

[167] J. R. Macdonald, "Power-Law Exponents and Hidden Bulk Relaxation in the
Impedance Spectroscopy of Solids," Journal of Elect r,: rl;..l..a~ l Clo, I,,. I ry, 378
(1994) 17-29.

[168] Z. K~erner and T. Pa-ilr. ;;i, !'!II'.. I I!1n of rough capacitive electrode: role of surface
disorder," Journal of 1..~ It.i ,t ,: l;,d...rl C'i, in:- i ry, 448 (1998) 139-142.

[169] C. Hitz and A. Lasia, "Experimental study and modeling on impedance of HER on
porous Ni electrode," Journal of 1.. !~ Ir...rtrl;,d... rl C'i, in,.i ry, 500 (2001) 213-222.

[170] J.-B. Jorcin, M. E. Orazem, N. Pi~bi~re, and B. Tribollet, "CPE Analysis by Local
Electrochemical Impedance Spectroscopy," Electrochimica Acta, 51 (2006) 1473-
1479.

[171] V. M.-W. Huang, V. Vivier, M. E. Orazem, N. Piibi~re, and B. Tribollet, "The
Apparent CPE Behavior of a Disk Electrode with Faradaic Reactions," Journal of
the Electrochemical S -. .:. Iri, 154 (2007) C99-C107.

[172] M. Mazurek, N. Benker, C. Roth, T. Buhrmester, and H. Fuess, "Electrochemical
Impedance and X-Ray Absorption Spectroscopy (EXAFS) as In-Situ Methods to
study the PEMFC Anode," Fuel Cells, 1 (2006) 16-20.

[173] A.-K(. Meland, S. K~jelstrup, and D. Bedeaux, "Rate Limiting Proton Hydration
in the Anode of the PEM Fuel Cell," Journal of M~embrane Science, 282 (2006)
96-108.

[174] J. Labato, M. A. Rodrigo, J. Linares, and K(. Scott, "Effect of the Catalytic Ink
Preparation Method on the Performance of High Temperature PEM Fuel Cells,"
Journal of Power Sources, 157 (2006) 284-292.

[175] K(.-T. Jeng, C.-C. Chien, N.-Y. Hsu, W.-M. Huang, S.-D. Chiou, and S.-H. Lin,
I III. !cation and inpedance studies of DMFC anode incorporated with CNT-
supported high metal content electrocatalyst," Journal of Power Sources, 2007
(2007) 33-41.

[176] A. Bieberle and L. J. Gauckler, "Reaction Mmechanism of Ni pattern anodes for
SOFC," Solid State lonics, 135 (2000) 337-345.










I I I I I


ligiligil


10 -0.6 .--o


E l o-2 0000 0.63 ,o
o O 0.3 A cm.Z
C: a 0.5 A cm-' 6 .0 o
N~10-3~ O 0.7 Acm'2
N O 0.9 A cm'2 o*
Q 1.1 Acm-' 0.57-
-04 LO
101 100 101 102 103 0.2 0.4 0.6 0.8 1.0 1.2
fI Hz Current Density / A cm-2
(a) (b)

Figure 8-2: Representation of the graphical analysis of the data presented in Figure 8-1
to obtain the CPE exponent c0: a) the magnitude of the imaginary part of the impedance
as a function of frequency with current density as a parameter; and b) CPE exponent
obtained from the slope of part (a) at high frequencies.


as proposed by Orazem et al.,224 where Zj is the imaginary part of the impedance, and

f is the frequency in units of Hz. The value of Qeaf is presented in Figure 8-3(a) as a

function of frequency with current density as a parameter. The frequency dependence of

the apparent CPE coefficient, evident at frequencies below 50 Hz, is caused by Faradaic

and transport processes. Faradaic and transport processes have negligible influence at

higher frequencies. The value of Qeaf was obtained by estimating the high-frequency

.I-i inia. J.-' of Figure 8-3(a) by calculating the average of the 10 values at the highest

frequencies.

The interfacial capacitance Ceaf was calculated by

rCe =n [eR1-a (8-2)



as derived by Brug et al.,15s where R, is the electrolyte resistance calculated from the

high-frequency part of the impedance data presented in Figure 8-1. In a comparison

of expressions developed by Hsu and Il I Is-1. 111'- and Brug et al.,15s Huang et al.17

found that equation (8-2) provided an excellent assessment of interfacial capacitance for

systems for which the CPE behavior originated from nonuniform current and potential

distributions along the electrode surface. Values of interfacial capacitance Ceaf obtained











0.4 III 1.05 ,aa
0.90-
0.3
0.75-

E 0. I E 0.60-
c; 0.1 a$c 0.45-
N d N 0.30-
0.0
0.15-
-0.1 1il 0.00 ill
10-3 10-2 101 100 101 102 103 10-3 10-2 10100 10' 102 103
flHz flHz

(a) (b)

Figure 4-8: Regression of the Voigt model to the imaginary part of the impedance cor-
responding to the first of five scans given in Figure 4-3: a) fit to the imaginary part of
the measurement, and b) prediction of the real part. The 0 represents the experimental
data, the heavy solid line represents the measurement model fit, and the thin solid lines
represent confidence intervals.


4.2.3 Evaluation of Low-Frequency Bias Errors

To test the consistency of the impedance data at low frequency, the imaginary part

of the impedance data was fitted using a weighting strategy based on the empirical model

for error structure given as equation (4-1). The parameter set so identified was used to

predict the real part of the impedance. The confidence interval for the prediction was

obtained by a Monte Carlo simulation based on the confidence interval of the regressed

parameters. The procedure is described by Awarwal et al.126

The Voigt measurement model was regressed to the imaginary part of the impedance

data corresponding to the first scan of the impedance data presented in Figure 4-3. The

results, given in Figure 4-8(a), show that the measurement model could provide an

excellent fit to the imaginary part of the data, even at the low frequencies that revealed

inductive loops, characterized by positive values of imaginary impedance. The parameter

values obtained from regression to the imaginary part of the impedance were used to

predict the real part, as shown in Figure 4-8(b). The solid lines shown in Figure 4-8(b)

represent the upper and lower bounds of the 95.4 percent (2o-) confidence interval obtained










-0 20 -0 20 co o
O New Channel oo o
-01 ai Interdgtaote d o o



Z/Acm2 Z/Ocm


(a) (b)

Figure 3-17: Impedance response of the new flow channel with 850C for H2 aS TreCtREL
at the anode and air as oxidant at cathode. The anode and the cell temperatures were
set at 50 oC and the cathode temperature at 45 oC. The fuel cell was assembled with a
uniform porous GDL; a) impedance response generated for the new channel as a function
of current density; and b) impedance response recorded at 0.4 A/cm2 for the two channels.


1. Contact resistance: The higher HFR manifested in impedance response of the

new channel could be ascribed to poor contact between the channel and the MEA.

2. Mass transport limitation: The low limiting current observed using the post

channel may be attributed to poor water management.

3. Flooding: Excessive noise discerned in the impedance response at higher current

densities could be attributed to stochastic processes such as floodingf.










independent of the type of measurement model used.134 While the regressed parameters

may not he associated unequivocally with a set of deterministic or theoretical parameters

for a given system, the measurement model approach has been shown to represent ade-

quately the impedance spectra obtained for a large variety of electrochemical systems.124

Regardless of their interpretation, the measurement model representation can he used to

filter and thus identify the non-stationary (drift) and high-frequency (noise) components

contained in an impedance spectrum.

The measurement model has been applied in previous work to assess the error struc-

ture of a variety of systems including electrohydrodynamic impedance,l electrochemical

impedance data for reduction of ferricyanide on a Pt rotating disk,1 6 for corrosion of cast

iron in Evian water,'se for corrosion of aluminum in orange juice,127 and for charging of

electroactive polymers.l3

2.4.2 Interpretation Model

mathematical models are needed to interpret the impedance data, including the

low-frequency inductive loops, in terms of physical processes. Gomadam et
reported an exclusive review of important literature for different approaches to model

the impedance response of the fuel cell and have also presented a concise comparison of

continuum-mechanics-based and equivalent-circuit based approach modeling. The most

quantitative of the impedance models reported in the literature have emphasized detailed

treatment of the transport processes, but use of simple electrochemical mechanisms

precluded prediction of the inductive loops. As the oxygen reduction reaction (ORR) at

the cathode is the rate-determining step, most models emphasize the reaction kinetics

at the cathode. The one-dimensional models proposed by Springer et
the cathode to be a thin film on ......1..1... 1 IrLed catalyst particles. They studied the role of

water accumulation in the gas diffusion 1loi;r and oxygen diffusion in the gas phase. These

models considered only a single-step irreversible OR R at the cathode. The impedance

models by other re-, 1.!.0. I '1114:3 also treated a single-step kinetics for the ORR.










CHAPTER 8
EVALUATION OF INTERFACIAL CAPACITANCE

Graphical methods were used to extract values of CPE parameters and interfacial

capacitance from impedance data collected on a PEM fuel cell. The impedance data

were recorded as a function of current density, time, temperature, backpressure, and

flow channel and gas diffusion 1 e. -r design. The value of the interfacial capacitance was

reduced when the cell was operated under dry or flooded conditions. The interfacial

capacitance decreased with time over a timescale consistent with the approach to a steady

state. In addition to providing an insight into physical processes, the parameters obtained

from graphical methods can he used for model reduction when regressing impedance

data. The methodology presented can he applied to any electrochemical system on which

impedance measurements can he conducted.

8.1 Introduction

Use of CPE parameters is frequent, though parameters estimated by fitting circuit

models to impedance data are not unique. The object of this work was to use the graph-

ical methods described by Orazem et al.224 to evaluate the influence of operation and

design parameters on the interfacial capacitance of a PEM fuel cell. The transient behav-

ior of CPE parameters was also investigated. The parameters obtained by the graphical

methods were used to explore processes such as flooding, drying, and catalyst deactivation

in the fuel cell.

8.2 Results

Typical impedance results are presented in Figure 8-1 with current density as a

parameter. The measurement model developed by Agarwal et
analyze the error structure of the impedance data.194'225 As shown by Roy and Orazem,194

data collected above a frequency of 1 kHz were inconsistent with the K~ramers-K~ronig

relations. This inconsistency was attributed to instrumental artifacts. Once a steady

operation had been achieved, the data collected at frequencies as low as 1 mHz were found

to be consistent with the K~ramers-K~ronigf relations. Data found to be inconsistent with












0.4-
I : 1 0.08 -0
N rN o
0.2 -O ,





N- -0. -0.04


10-3 10-2 10100 10' 102 103 10-3 10-2 10100 10' 102 103
flHz flHz

(a) (b)

Figure 4-9: Normalized residual errors for the regression presented in Figure 4-8: a) fit
to the imaginary part, where dashed lines represent the +2a bound for the stochastic er-
ror, and b) prediction of the real part, where solid lines represent the 95. !' confidence
intervals for the model obtained by Monte Carlo simulations.


for the model prediction. The low-frequency data that are outside the confidence interval

can therefore be considered inconsistent with the K~ramers-K~ronig relations.

A more precise view of the regression quality and the level of agreement with the

predicted values can be seen in plots of residual errors. The normalized residual error

for the regression to the imaginary part of the impedance is shown in Figure 4-9(a)

where the dashed lines indicate upper and lower bounds for the stochastic noise level

for the measurement. The dashed lines were calculated as +2a where a was obtained

from equation (4-1). The normalization by the experimental value of the impedance

causes the dashed lines to tend toward +00 at the point where the imaginary impedance

changes sign. The quality of the regression is indicated by the observation that the

residual errors for the regression fall within the noise level of the experiment. The

normalized residual errors for the predicted real value are shown in Figure 4-9(b), where

the solid line represents the upper and lower bounds of the 95.4 percent (2a) confidence

interval obtained for the model prediction. A lack of agreement between predicted and

experimental values is seen for frequencies below 0.05 Hz. The data for the four lowest










A great number of polymer materials have been prepared and functionalised for

possible electrolytes for fuel cells. Improvements in the membrane structure and conduc-

tivity were achieved by producing composite membranes. Usually, PTFE is added into

Nafion to improve mechanical strength, therefore much thinner 1... -r of PTFE blended

Nafion can be used which has advantage of low Ohmic drop as compared to pure Nafion.

However, thinner PTFE doped Nafion has larger permeation rate thus low OCV.22 The

larger permeation results in higher crossover of reactants, and heat generated by reaction

due to local hot spots create localized membrane drying, and higher membrane resistance.

The crossover of reactants have been utilized to make these membrane self-humidifying by

providing highly dispersed Pt particles in the membrane which enables localized formation

of water though uniform distribution of Pt is not achieved. To exploit this idea, very thin

1... ris of Pt/C have been used both side of the membrane which reduces the crossover as

well as ensure formation of water to humidify membrane.22

Also, a compound C-~ -Ho.sPW12040 has been investigated to incorporate into

Nafion/PTFE composite, better performance observed is attributed to strong acidic

and hydrophilic nature of the compound which enhance water retention capacity.23 A

composite membrane by blending Nafion with poly(vinylidene fluoride) is investigated

though the observed proton conductive is much lower than Nafion which is due extreme

hydrophobicity of fluoride components. To improve water affinity and proton conductivity,

the composite is chemically modified by dehydrofluorination and treatment with H2SO4-24

W.L. Gore and Asahi C!. un.! II< have successfully reinforced perfluorosulfonic acid

membranes with Teflon fabric.25 Carbon nanotubes have been proposed to incorporate

into Nafion to increase mechanical stability due to their exceptional enforcing fibre

strength, low density and high aspect ratio, however, since carbon is electronic conductor

which can lead to electronic short-circuit thus reducing the OCV.26

By operating fuel cells at higher temperature, the oxygen reduction kinetics and

carbon monoxide poisoning problems are improved. Composites are made by swelling












C,-, .-


GDL- CAL .membrane CAL GDL

H2 02, H20


Anode Cathode

Figure 5-1: A schematic representation of the relationship between the fuel cell geome-
try and an equivalent circuit diagram for proposed reaction sequences where the boxes
represent Faradaic impedances determined for specific reaction mechanisms.


Faradaic impedances that are to be determined for the specific assumed reaction mecha-

nisms. Three impedance models were investigated for the interpretation of low-frequency

inductive loops. Model 1 incorporates a single-step ORR at the cathode and a single-step

HOR at the anode. Model 2 treats hydrogen peroxide formation in a two-step ORR at the

cathode along with a single-step HOR at the anode, and Model 3 includes the single-step

OR R coupled with the platinum catalyst dissolution at the cathode along with a single-

step HOR at the anode. The literature -II_ _- -; that the rate should be of the order of 3/2

with respect to proton concentration and of the order of 1 with respect to the oxygen con-

centration.144 For the present work, the surface concentration of the proton was assumed

to be constant and was therefore incorporated into the effective reaction rate constant.

5.4.1 Model 1: Simple Reaction Kinetics

The OR R

()2 + 4H+ + 4e- 2H120 (5-15)









Abstract of Dissertation Presented to the Graduate School
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Doctor of Philosophy

USE OF IMPEDANCE SPECTROSCOPY TO INVESTIGATE FACTORS THAT
INFLUENCE THE PERFORMANCE AND DURABILITY OF PROTON EXCHANGE
MEMBRANE (PEM) FUEL CELLS

By

Sunil K(. Roy

August 2008

C'I ny~: Mark E. Orazem
Major: Chemical Engineering

Impedance spectroscopy provides the opportunity for in-situ identification and

quantification of physical processes and has been used extensively to study the behavior of

the fuel cell. However, a key question to be answered is whether the features seen in the

impedance response are caused by an artifact or represent a physical process taking place

in the system. The measurement model developed by our group can be used to identify

the frequency ranges unaffected by bias errors associated with instrument artifacts and

non-stationary behavior.

Impedance measurements were performed with the 850C fuel-cell test station supplied

by Scribner Associates and with a Gamry Instruments FC350 impedance analyzer coupled

with a Dynaload electronic load. All electrochemical measurements were performed

with a two-electrode cell in which the anode served as a pseudo-reference electrode. The

experiments were conducted in galavanostatic mode for a frequency range of 0.001-3000

Hz with 10 mA peak-to-peak sinusoidal perturbation, and ten points were collected per

frequency decade. Ultra pure hydrogen was used as the anode fuel, and compressed air

was used as oxidant.

The measurement model was used to show that low-frequency inductive loops were,

in some cases, fully self consistent, and, therefore, the inductive loops could be attributed

to processes occurring in the fuel cell. Then we developed first-principle models that









iT = io2; [current at cathode]

ih2 = iT; [current at anode]

na = (log((iT)./(Kh2. Ombulkh2). (1 (iT./ilimb2))))./bh2; [equating current at

cathode and anode]

VT = V (iT. Re ff) + na; [cathode overpotential]

plot (iT, VT,' -') ;

plot (iexp, eexp,' o');
Rio = [(2(cao)F2(1 3I)O)/(RT)]; [C'l. .I-ge-transfer resistance for ORR]

Rth = [(2(ash)F2(y)H)/(RT)]; [C'l. .I-ge-transfer resistance for HOR]

pO = (2Fkoexp,(-aoFV/(RT))); \!l I---transfer impedance for ORR]

q0 = (2Fkhexp,(-caaFV /(RT))); \l I-+ltransfer impedance for HOR]

w = -6 : .05 : 6; [Frequency range]

w =10.";

pl = Rio;
K~h2 = (w + delta2)/dh2; [tangent hyperbolic for Hydrogen]

th2 = tanh(sgrt(i + Kh2))./(sgrt(i + Kh2));

Ko02 = (w. + delta2)/do2;

to2 = tanh(sgrt(i + Ko2))./(sgrt(i + Ko2));

Al = 1./(RtO2 + ZDO2 + to2); [lumped parameters for HOR]

C1 = 1./(RtH2 + ZDH2 + th2); [lumped parameters for HOR]

p2 = pO;

q1 = Rth;

q2 = q0;

z1 = (pl q1). (p2 q2);

z2 = zl./((jwF2) p2 q2);

z3 = z2 + (pl + q1) + (jwc);

z4 = 1./z3;










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Solid Acid Composite Membranes for Fuel-Cell Applications," Journal of the
Electrochemical S -- .:. Iri, 147 (2000) 3610-3613.

[35] R. Jiang, H. R. K~unz, and J. M. Fenton, "Composite Silica/Nafion Membranes
Prepared by Tetl I. Ir:lorthosilicate Sol-Gel Reaction and Solution Casting for
Direct Methanol Fuel Cells," Journal of M~embrane Science, 272 (2006) 116-124.

[36] M. A. Sweikart, A. M. HE vliin_ J. A. Turner, D. L. Williamson, B. D. McCloskey,
S. R. Boonr-icnr and M. Sanchez, "12-Tungfstophosphoric Acid Composites with
Sulfonated or Unsulfonated Epoxies for High-Temperature PEMFCs," Journal of the
Electrochemical S -. .:. Iri, 151 (2005) A98-A103.

[37] A. P. Saab, F. H. Garzon, and T. A. Zawodzinski, "Determination of Ionic and
Electronic Resistivities in Carbon/Polyelectrolyte Fuel-Cell Composite Electrodes,"
Journal of the Electrochemical So .:. I i, 149 (2002) A1541-A1546.

[38] A. Rusanov, Nu \i-, 1 Bis(N I1I1.11. .Inc Anhydrides) and Their Polyheteroarylenes with
Improved," Adv. Polym. Sci., 111 (1994) 115-175.

[39] C. Feger, J. McGrath, and M. K~hojasteh, P JI;;.:I,.:ll. Materials, Clo, I,,.--iry and
C'l,;r,,. I. rization (Elsevier: New York, 1988).

[40] X. Wang and I.-M. Hsing, "Surfactant Stabilized Pt and Pt Alloy Electrocatalyst for
Polymer Electrolyte Fuel Cells," Electochimica Acta, 47 (2002) 2981-2987.










nanotubes. To overcome this problem, catalyst support based on carbon aerogel-based was

explored and better performance was observed.54

Gold has been also investigated as a possible catalyst support which shows compa-

rable electrochemical active area and so the performance with Carbon on much lower Pt

loadings though the cost of Gold is a concern.57 A conducting polymer comp< .-!I ~' for

catalyst support material, was tested. The composite consists of an electronic conductive

end (e.g. polyprrole, poly (3,4-ethylenedioxythiophene) ), and a proton conducting end (e.g.

pub'l--ri-i. in. -II1Cun Ir,e). It has excellent performance for oxygen reduction reaction however;

a decimal performance is observed for hydrogen oxidation because at anode potential the

electronic conducting functional group becomes inactive. Tungsten Oxide (WO3) WaS alSO

proposed as a possible catalyst support as it is a stable oxide and not prone to PtO for-

mation compared to conventional catalyst support.59 1 IS 1S lo more thermally stable than

Carbon which enables its use in high temperature operation of the fuel cell. Polyaniline

doped trifluoromethane sulfonic acid is investigated as a proton conducting material to be

used in catalyst instead Nafion. Its fibrous nature helps distribute particles uniformly, and

ensures better connection of reaction sites, and thus enhances Pt utilization compared to

Nafion.

Optimization of catalyst composition with respect to Pt, and Nafion loadings has

been investigated thoroughly. An optimal composition of Nafion has observed; to little

Nafion was insufficient for proton conduction thus increases ionic resistance, on the other

hand, too much Nafion, may cover Pt particles forming a films that hinders electron

transport to Pt therefore reduces catalyst utilization. Also, it fills carbon pores hindering

gas transport and water removal. Since Nafion is not mechanically stable at higher water

content so in case of flooding too much Nafion can lead to break-down of catalyst 1.v. r.

Nafion loading usually results in Ohmic and mass-transport (diffusion) limitation in the

fuel cell operation.










evident at current densities above 1 A/cm2 for the MEA with a non-uniform GDL and at

current densities above 0.3 A/cm2 for the MEA with a uniform GDL. Drying was evident

at current densities below 0.3 A/cm2 for the MEA with a non-uniform GDL.

The work presented here demonstrates that the stochastic error structure of

impedance measurements may be used to detect operating conditions of the fuel cell

which induce flooding or drying. In this case, the flooding or drying phenomena con-

tribute stochastic errors which are superposed on those associated with the electronic

instrumentation.

9.5 Evaluation of Interfacial Capacitance

Graphical methods were used to interpret impedance spectra in terms of CPE pa-

rameters, and the formulas presented by Brug et al.227 Were used to convert these into

effective interfacial capacitance. The effective interfacial capacitance was smallest at small

and large current densities and showed a maximum value at the intermediate current

densities. The decreases in interfacial capacitance with higher current density can he

attributed to an excess production of water resulting in flooding; whereas, at low current

density, the effect could be attributed to drying. The interfacial capacitance was depen-

dent on flow channel configuration, GDL properties, temperature, and backpressure. The

improved performance and larger interfacial capacitance observed for the interdigitated

flow channel and the non-uniform GDL could be attributed to the improved water man-

agement capabilities of these system designs. A smaller influence of time was observed

which could be associated with the long time required to achieve steady-state operation.194

The use of graphical methods to extract physical properties is under-utilized in the

fuel cell literature. The method provides unequivocal values for the CPE exponent c0,

the CPE coefficient Q, and the Ohmic resistance R,. The interpretation of the resulting

parameters in terms of interfacial capacitance is, however, less clear. More work is needed

to confirm the suitability of the Brug formula for combined 2-D/:3-D distributions present

in the PEM fuel cell.










Paganin et
been superimposed on the higher-frequency are. The overall impedance response has been

explained as the effect of the double- lai-< v capacitance and the charge transfer resistance

of oxygen reduction reaction (ORR). Song et
for the impedance response of the fuel cell. Impedance response reported by Springer et


impedance response of the fuel cell with different cell voltage, humidification temperature

of reactants, and airflow rate. They have reported impedance spectra with two loops:

the high-frequency loop was attributed to the effect of reaction kinetics and oxygen

transport in the CAL, and the low-frequency loop was attributed to mass transport

limitations of gases and water in the GDL. The group has also -II_0-r-- -1.. a circuit analog

model to explain the experimental results and have calculated the parameters such as

surface exchange current density and Tafel slopes. 1\any authors e.g.. Castanita et al.ls6

and Li et al..62 reported only one capacitive loop. Castanna et
exponential decrease in the charge transfer resistance with increases in the overpotential.

They also have reported the decreases in the double- lai-< v capacitance with the increases

in the overpotential and the capacitance reaches a constant value once the performance is

controlled by ohmic effects. The higher value of the capacitance observed in the kinetics

control region could be due to charging-discharging processes in the region.

Some research groupS119-12:3 have also used the impedance to characterize CO toler-

ance of the fuel cell. Jiang et
tolerance of electron Ir Ilh--r as a function of DC hias potential, temperature and relative

humidity while K~im et al.120 have used the impedance to investigate the effect of CO

on the performance of the fuel cell and have reported that charge-transfer resistance as

well as hydrogen dissociation resistance increase with an increase in the CO concentra-

tion but it has little effect on low frequency are of the impedance spectra. Yang et
have applied a three-electrode arrangement to investigate effect of the CO on the fuel









was assumed to take place at the cathode. The steady-state current density expression

corresponding to this reaction was assumed to be


io, = -KozCOz(0) exp (-bo, r0, ) (5-16)


where Ko, = nFko,, ko, is the rate constant, a = 4 is the number of electron exchanged

in the reaction, bk, = Gk~FIRT, Gkr is the apparent transfer coefficient for reaction k, R

is the universal gas constant, T is absolute temperature, Ci(0) is the concentration at

electrode surface, rli = V Veqi, ri is the surface overpotential, and Veq.,i is the equilibrium

potential.

The single-step HOR

H2 2H+ + 2e- (5-17)

was assumed to take place at the anode. The corresponding steady-state current expres-

S10n WaS

iHz = KH2CH, (0) exp (bH, rlHz) (5-18)

where KHz = nFkH2, kH, iS the rate constant, and n = 2.

The overall impedance was calculated as

1 1
Z = Re + + (5-19)
(Rt,Hz ZD,H j-1 tL(,C, (,~O, +ZD~,O i-1 j

where Re is the frequency independent ohmic resistance, Co,c is the interfacial capacitance

at the cathode, Qo,, is the interfacial capacitance at the anode, Rt,o, is the charge-transfer

resistance for the ORR, i.e.,


Rtoo, [Ko2Eo? (0)bo2 exp(-bo,902)] (5-20)


ZD,O, iS the mass-transport impedance for the ORR, i.e.,

60 -1
ZD,Oz O (5-21)
co, (0)bo, 4FDoz 8o,(0)
















0.0 0.1 0.2 0.3 0.4 0.5


-0- Fresh MEA
-n- Used MEA


0.8-


0.6-


0.4-


Current Density / A cm-2


Figure :3-11: Polarization curve generated front the steady-state measurement as a func-
tion of time with 850C for H2 as reactant at the anode and air as oxidant at cathode. The
anode reactant stream and cell temperatures were set at 40 oC and the cathode reactant
stream temperature at :35 oC. The fuel cell was assembled with a serpentine flow channel,
and a uniform porous GDL.


-1.5 .- L



E-1.0 -/
o -0- Fresh MEA
-0. -6- Used MEA


N 0.0-
0 1 2 3 4 5 6
Z / cm2


Figure :3-12: Impedance responses collected as a function of times a function of time with
850C for H2 as reactant at the anode and air as oxidant at cathode. The anode reactant
stream and cell temperatures were set at 40 oC and the cathode reactant stream temper-
ature at :35 oC. The fuel cell was assembled with a serpentine flow channel, and a uniform
porous GDL.











TABLE OF CONTENTS

page

ACK(NOWLEDGMENTS ......... . .. .. 4

LIST OF TABLES ......... ..... .. 8

LIST OF FIGURES ......... .... .. 9

LIST OF SYMBOLS

ABSTRACT ... ......... .............. 19

1 INTRODUCTION ......... .. .. 21

2 LITERATURE REVIEW ......... .. .. 22

2.1 Electrochentistry and Losses in the Fuel Cell ... .. .. .. 2:3
2.1.1 Activation Loss ......... .. .. 25
2.1.2 Ohmic Potential Loss ....... ... .. 26
2.1.3 Concentration Overpotential Loss ... .. .. 26
2.1.4 Parasitic Potential Loss . ..... .. 27
2.2 PEM Fuel Cell Components ........ ... .. 28
2.2.1 Membrane ......... . .. 28
2.2.2 Electrodes ......... . .. :32
2.2.3 Gas Diffusion L n. ris ........ ... .. :36
2.2.4 Bipolar Plates ........ .. .. .. :37
2.3 Degradation Mechanisms in Fuel Cells ..... ... .. :39
2.3.1 Hydrogen Peroxide Formation ...... .. .. :39
2.3.2 Platinum Oxidation and Dissolution .... .... .. 41
2.4 Electrochentical Impedance Spectroscopy .. .. 44
2.4.1 Measurement Model Analysis ...... .. . 45
2.4.2 Interpretation Model ........ ... .. 47
2.4.3 Flooding in the Fuel Cell . ..... .. .. 49
2.4.4 Evaluation of Interfacial Capacitance .... .. .. 50

:3 EXPERIMENTAL ......... .. .. 52

:3.1 Introduction ......... . .. .. 52
:3.2 Experimental ......... ... .. 56
:3.2.1 Materials and Chemicals . ..... .. .. 56
:3.2.2 Electrochentical Impedance Measurements ... .. .. 58
:3.2.3 Other Electrochentical Techniques .... .... .. 59
:3.2.4 Surface Analysis ......... .... .. 59
:3.2.4.1 Scanning electron microscope ... .. .. 60
:3.2.4.2 Transmission electron microscope .. .. .. 60
:3.2.4.3 X-ray photoelectron spectroscopy ... .. . .. 60
:3.3 Results .......... ......... 61





























(a) (b)


Figure 5-2: Equivalent circuit diagrams for proposed reaction sequences where the boxes
represent diffusion impedances or Faradaic impedances determined for specific reaction
mechanisms: a) anode for all models; b) cathode for Model 1; c) cathode for Model 2; and
d) cathode for Model 3.


Cathode,
Model 1:


Anode:


Cathode,
Model 2:


Cathode,
Model 3:



0,c



-Zo2


0,c



-
- zo2

-
- zH202
(c)











1.2 gga

1.0

0.8

0.6 -p
,J oo
04- O Experimental data
0 Model 2
0. -~, Model 3

0.0-

0.0 0.5 1.0 1.5 2.0 2.5
Current / A



Figure 5-7: Polarization curve generated by Models 2 and :3 for 40 oC using parameters re-
ported in Table 5-1 and compared with the experimental data presented in Figure 5-:3(a).


that accounts for only the hydrogen oxidation and oxygen reduction reactions cannot

explain the inductive behavior at low frequencies.

5.5.2.2 Models 2 and 3

The polarization curves generated with Models 2 and :3 are presented in Figure 5-7.

The presence of the side reactions in the model has little discernable influence on the

polarization curve because these reactions are assumed to be taking place at a low rate

as compared to the dominant hydrogen oxidation and oxygen reduction reactions. The

relative contributions of the different reactions at the cathode are shown in Figure 5-8.

As shown in Figure 5-8(a), the two reduction steps in Model 2 contributed equally to the

total current because the desorption/loss of peroxide was not considered in the model

development. The contribution to total current by platinum dissolution shown in Figure

5-8(b) was found to be negligible as compared to oxygen reduction.

The impedance response for the model with the hydrogen peroxide formation (Model

2) consisted of one high-frequency capacitive loop and one low-frequency inductive loop.

The impedance response for the model accounting for platinum dissolution (Model :3)

also consisted of one high-frequency capacitive loop and one low-frequency inductive










0.1 I 20 Hz

-0.3 a 0.7 A cm-2


-0.2 ~0.2

-oi 1 kHz .

0.1 -0.005 Hz
0.00 0.15 0.30 0.45 0.60 0.75 0.90
Z / cm2

Figure 7-12: The impedance data recorded using the MEA with a uniform GDL. The
anode, the cathode, and cell temperatures were set at 50 oC.


Similar experiments and analysis were performed on the MEA with a uniform GDL.

The impedance response is presented in Figure 7-12 with current density as a parameter.

The scattering at higher current densities was more evident than observed for experiments

using the non-uniform GDL. Transient single-frequency impedance measurements were

used to obtain the standard deviations for real and imaginary parts of the impedance.

The standard deviation for the real part of the impedance is presented in Figure 7-13 as

a function of current density for frequencies of 0.1, 10, and 100 Hz. The base-line error

structure model used to normalize the data was calculated at a current density of 0.2

A/cm2

7.2.2.4 Detection of dry conditions

The stochastic errors for small current densities are shown in Figure 7-14 for the

MEA with a non-uniform pore distribution. The empirical model given by equation (7-

1) provided a good description for the behavior at a current density of 0.4 A/cm2, but

the observed errors are much larger for lower current densities where dry conditions are

anticipated. This result is consistent with the experimental observations of Schneider et

al.1ss who report impedance scans with large scatter at low frequencies for dry conditions.

The standard deviation of the real part particularly at low frequency, however, can be

used as well to detect the presence of dry conditions.









3.3.6 Flow Channel as a Parameter

The reactant flow channel design is one of the prominent factors that influences

mass-transport. Condensed water may be removed by gas flow. Thus, changes in reactant

flow channel design have been proposed to reduce the flooding. A comprehensive review of

various flow-field designs developed by researchers and companies has been reported in the

literature.199 Several authorS149,200-205 have investigated performance of the fuel cell with

different flow channels and have reported better performance in case of an interdigfitated

flow channel. Hsieh et al.200 has reported better performance in case of an interdigitated

channel as compared with a serpentine flow pattern in the fuel cell although they have

proposed a new flow design. The better performance of the interdigfitated flow channel

was interrelated as a result of convective flow promoted by the interdigitated flow design

which allowed a better utilization of catalyst.201 The local concentration polarization due

to non-uniform distribution of reactants in a parallel flow pattern is possible reason of

less performance as compared to a serpentine channel in the fuel cell.202 The theoretical

study reported by K~azim et al.206 has showed that the limiting current density of the

fuel cell with an interdigitated flow field was about three times the current density with a

conventional flow field.

In spite of the fact that the interdigitated flow field performs better, very limited

experimental studies have been published. Wang et al.4 has presented a systematic

experimental study on the performance of the fuel cell with an interdigitated flow field

by investigating the effect of cell temperature, gas humidification, operating pressure

and reactant gas flow rates. The interdigfitated flow field has advantage of convective

transport in addition of the diffusive and capillary transport in the conventional flow fields

though the pressure drop created between non-interconnecting inlet and outlet, promotes

floodingl49 because the pressure in downstream is low, which pose difficulty in removing

water. There have been several theoretical studieS73,74, 150,207 published to address the









following two half-cell reactions (2-1) and (2-2) take place at the anode and the cathode

respectively, and equation (2-3) is the overall reaction in the fuel cell.


H2 2H+ + 2e- (2-1)


02 + 4H+ + 4e- 2H20 (2-2)

02 + 2H2 2H20 (2-3)

The main components of the fuel cell are shown in Figure 2-1(b). The fuel cell typically

consists of a membrane, two electrodes, gas diffusion le r-is (GDL), and bipolar plates.

2.1 Electrochemistry and Losses in the Fuel Cell

The change in Gibbs free energy (AG) is measure of the maximum work obtainable

from the reaction. AG for the overall reaction (2-3) in the fuel cell is -237.14 kJ/mole at

standard conditions. Cell potential can be calculated by equation (2-4).


AG = nFEo (2-4)


where F is Faraday constant equals to ;II I C/mole, n is number of moles of electrons

involved in the reaction, and Eo is electrode potential. Equation gives value of cell

potential as 1.23V which is referred as an open circuit voltage (OCV). AG is a function

of operating conditions such as operating temperature and pressure, hence the OCV

also depends on the operating conditions of the cell. The dependency of the potential is

described by the N. I is-1 equation which gives the thermodynamic voltage of fuel cells.

RT PI, 25
Enemnst = Eo+ In( )(25
nF Poi

where R is Universal gas constant, T is temperature, Pi is pressure for i reactants. The

actual voltage output of a fuel cell is less than the thermodynamically predicted (N. Its-1

Equation) voltage due to several irreversible losses.2 A plot of cell voltage versus current

density known as polarization curve (Figure 2-2), which shows various losses taking

place in the fuel cell. The actual voltage drawn from the fuel cell should be equal to the











1.0-

0.8-

S0.6C -

O Experimental data 0
C 0.4 -O
m Model 1
0- 0.2-

0.0-

0.0 0.5 1.0 1.5 2.0 2.5
Current / A




Figure 5-4: Polarization curve generated by Model 1 for 40 oC using parameters reported
in Table 5-1 and compared with the experimental data presented in Figure 5-3(a).


5.5.2.1 Model 1

The polarization curve generated from Model 1 is compared to experimental data in

Figure 5-4. The parameters used to generate the polarization curve were then used to

calculate the impedance response. The results for an intermediate-current (0.2 A/cm2) arT

compared in Figure 5-5 to the experimental data. The impedance response for Model 1

consisted of one compressed capacitive loop with a straight-line portion at high frequency.

Similar impedance spectra have been reported in the literature.107,65,216 The capacitive

arc can be attributed to the single-step ORR at the cathode. The straight-line portion

at the higher frequencies can be attributed to mass transport impedance associated with

diffusion of oxygen. Model 1 provides a reasonable representation of the capacitive loops,

but cannot account for the inductive loops seen at low frequency.

The inability of Model 1 to account for the low-frequency inductive loops is seen more

clearly in Figures 5-6(a) and 5-6(b), where the real and imaginary parts of the impedance

are presented, respectively, as functions of frequency. Model 1 provided similar agreement

to the experimental results at both lower and higher current densities. Thus, the model












1.0-

-,0.8-

S0.6-

S0.4-

0.2 *sl*I
0.0 0.1 0.2 0.3 0.4 0.5

Current Density / A cm-2


Figure 4-1: Polarization curve generated from the steady-state measurement with 850C for
H2 aS reactant at the anode and air as oxidant at cathode. The anode reactant stream and
cell temperatures were set at 40 oC and the cathode reactant stream temperature at 35
oC.


recently, Wiezell et al.145 COnSidered a two-step hydrogen oxidation reaction and reported

low-frequency inductive loops. They have explained that the inductive loops were the

result of changing different factors such as water concentration, membrane thickness,

hydrogen pressure and the hydrogen oxidation kinetics. The influence of carbon monoxide

poisoning on platinum and platinum-ruthenium anodes was investigated using impedance

spectroscopy."'7~I" The reported impedance response exhibited low frequency pseudo-

inductive behavior which was attributed to a surface relaxation process of competitive

oxidation of hydrogen and carbon monoxide at the anode.

The inductive loops reported in the literature are typically seen at very low frequen-

cies, e.g., 1 mHz, at which system stationarity must be questioned. The objective of this

work was to use the measurement model developed by Agarwal et al.124-127 to determine

whether the low-frequency inductive loops were due to or influenced by non-stationary

behavior.

The time required to make the measurement at each frequency is shown in Figure

4-2. The long time required at lower frequencies made measurements at these frequencies

susceptible to being influenced by nonstationary behavior.










CHAPTER 4
ERROR ANALYSIS OF IMPEDANCE RESPONSE

The measurement-model-based error structure analysis of impedance data is pre-

sented in this chapter.

4.1 Introduction

Impedance spectroscopy is often used to characterize processes in fuel cells, including

PEM fuel CellS.105,64,106-108 Low-frequency inductive featureS144'208'209 are commonly seen

in impedance spectra for the fuel cell (see, for example, Figure 3 reported by Makharia

et al.208). Alakhariadt
the fuel cell operation can he possible causes of the inductive loop seen at low frequency.

However, such low-frequency inductive loops could also be attributed to non-stationary

behavior, or, due to the time required to make measurements at low frequencies, non-

stationary behavior could influence the shapes of the low-frequency features. Impedance

spectra typically exhibit inductive features at high frequency, and some authors report

inductive loops at low frequencies. The high-frequency inductive features are understood

to be caused hv instrument artifacts, but the interpretation of the low-frequency inductive

loops is less clear. While the low-frequency loops have been tentatively attributed to side

reactions,146 they could also be caused or influenced by nonstationary phenomena. The

objective of this part of the work was to use the measurement model conceptl24-127 tO

assess the error structure of the impedance measurements taken for the fuel cell.

A recent impedance study reported by Makharia et al.208 TeVealed a capacitive loop

at intermediate frequencies and an inductive loop at low frequency. The capacitive loop

was attributed to the response of electrochemical reactions occurring in the fuel cell,

and the inductive loops were tentatively attributed to side reactions and relaxation of

associated reaction intermediates. Their interpretation is consistent with that -II_t-r-- -1..

by Antoine et al.,144 who proposed the presence of unspecified reaction intermediates.

They -II_ _t---- -1. that low-frequency inductive loops were a result of the relaxation of

adsorbed species involved in different steps of the oxygen reduction reaction. More









The formation of peroxide at cathode has been reported due to crossover of hydrogen

from anode to cathode. The effect of temperature and humidity on peroxide formation

kinetics was studied showing higher concentration of peroxide at the cathode compared

to at the anode.81 The peroxide formation inside the membrane was also observed due to

presence of platinum band.82 The formation of Pt band is possible due to dissolution and

migration of Pt particles from electrodes and redeposition inside membrane.

The hydrogen peroxide initiates formation of reactive radicals such as Hydroxyl and

hydroperoxyl in presence of Fe+3, CU+2, etC. aS folle 1../91,83


H202 + +2 ~ +3 + OH *+OH- (2-11)


H202 + OH* OOH +H20 (2-12)

To investigate the formation of these radical in the fuel cell, electron spin resonance

(ESR) study has been used by Endoh et al.84 They have also found that these radicals

degrade catalyst by attacking carbon in catalyst le -;r. These radicals attack side-chain

of membrane forming HF therefore fluorine emission rate (FER) is proposed as an

indication of membrane degradation.81,9,85 However, peroxide concentration can not

be directly related to membrane degradation because degradation results from a series

of reactions: formation of peroxide, followed by formation of radicals, finally attack

of these radicals on side-chain. Also, formation of radicals require presence of metal

ions.'" These ions are typical contamination from piping, tubes, and storage tanks of

the fuel cell. Fe+3 Can alSO arise from bipolar plate contamination.69 FER represents

material erosion and decomposition across the overall cell may not accurately reflect

local degradation of membrane which depends on local temperature, hydration level,

contamination concentration, etc.86 The formation of cross-linking S O S is reported

which can be due to dissolution of acidic group of Nafion (-SO3H, pendent side-chain)

provoked by peroxide leading to degradation."' The loss of acidic sites, reduction in

proton conductivity of membrane was observed.


















0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4


O-
,' `Q -o- 0.42 h
: a'o A 0.83 h
I 's 1.25 h


'
I
I


1.6 -

1.4 -

1.2 -

1.0-

0.8 -



0.4 .


E


'0--


'


o


0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6


Current Density / A cm-2


Figure 8-4: CPE coefficient Qenf as a function of current density with time as a parameter.
The impedance data were obtained under the conditions described for Figure 8-1.


0.18


.' s -- ---


--o
...o--- 0.42 h
:a 0.83 h -
S1.25 h


0.15 -



0.12 -



0.09-



0.06-


hi
E
o
LL


o


0.03


Current Density / A cm-2


Figure 8-5: The interfacial capacitance Cenf, obtained front equation (8-2), as a function of
current density with time as a parameter. The impedance data were obtained under the
conditions described for Figure 8-1.










:3-8 Galvanodynamic curves recorded at a cell temperature of 40 oC using the 850C
for H2 as reactant at the anode and air as oxidant at the cathode: a) hysteresis
curve for scan rate 50 mA/:30 s; and b) the flooding region of the hysteresis curve. 66

:3-9 The measurement recorded with the 850C for H2 as reactant at the anode and
air as oxidant at the cathode. The anode, the cathode and cell temperatures
were set at 40 oC; a) hysteresis curve for scan rate 50 mA/:30 Sec.; and b) impedance
responses as a function of current densities. ..... .. . 67

:3-10 The measurement recorded with the 850C for H2 as reactant at the anode and
air as oxidant at the cathode. The anode, the cathode and cell temperatures
were set at 50 oC; a) hysteresis curve for scan rate 50 mA/:30 Sec.; and b) impedance
responses as a function of current densities. ..... .. . 67

:3-11 Polarization curve generated from the steady-state measurement as a function
of time with 850C for H2 as reactant at the anode and air as oxidant at cath-
ode. The anode reactant stream and cell temperatures were set at 40 oC and
the cathode reactant stream temperature at :35 oC. The fuel cell was assembled
with a serpentine flow channel, and a uniform porous GDL. .. .. .. .. 68

:3-12 Impedance responses collected as a function of times a function of time with
850C for H2 as reactant at the anode and air as oxidant at cathode. The an-
ode reactant stream and cell temperatures were set at 40 oC and the cathode
reactant stream temperature at :35 oC. The fuel cell was assembled with a ser-
pentine flow channel, and a uniform porous GDL. .. .. .. 68

:3-13 The configuration of the post flow channel. .... .. .. .. 70

:3-14 Polarization curves generated for two flow channels from the steady-state mea-
surement with the 850C for H2 as reactant at the anode and air as oxidant at
the cathode. The anode and cell temperatures were set at 40 oC and the cath-
ode temperature at :35 oC. The fuel cell was assembled with a uniform porous
GDL. ..... ....... .......... ... 71

:3-15 Impedance responses collected with the 850C for two flow channels with the
850C for H2 as reactant at the anode and air as oxidant at the cathode. The
anode and cell temperatures were set at 40 oC and the cathode temperature at
:35 oC. The fuel cell was assembled with a uniform porous GDL. .. .. .. .. 71

:3-16 Polarization curves generated for the new and a conventional flow channels from
the steady-state measurement with the 850C for H2 as reactant at the anode
and air as oxidant at the cathode. The anode and cell temperatures were set at
40 oC and the cathode temperature at :35 oC. The fuel cell was assembled with
a uniform porous GDL. .. ... .. .. 72









Several models for the impedance response of PEM fuel cells have considered a

more detailed reaction mechanism. The model developed by Eikerling and K~ornyshev19

considered a single-step ORR to be reversible at the cathode. Antoine et al.144 has

proposed an impedance model with a three-step ORR kinetics in acidic medium on

platinum nanoparticles though reaction intermediates were unspecified and kinetics at

the anode was not considered in their model. They explained that the low-frequency

inductive loops were a result of the second relaxation of the adsorbed species involved

in the different steps of the ORR. More recently, Wiezell et al.145 COnSidered a two-step

hydrogen oxidation reaction (HOR) and have reported low-frequency inductive loops.

They explained that the inductive loops were the result of changing factors such as water

concentration, membrane thickness, hydrogen pressure and the HOR kinetics.

The role of intermediates in the ORR is supported by independent observation

of hydrogen peroxide formation in PEM fuel cells.7-9 A rotating-ring-disk-electrode

study"7 revealed that formation of the peroxide on platinum particles supported on

carbon (catalyst used in the fuel cell) is quite possible by two-electron reduction while

the formation is not an option on clean bulk platinum. The hydrogen peroxide formed

as an intermediate causes chemical degradation of the membrane.9 Other reactions

have also been reported which could potentially account for the low-frequency features

observed in the impedance data. Platinum dissolution, for example, has been observed in

PEM fuel cells'o which can lead to the loss of catalytic activity and, consequently, to the

degradation of the fuel cell performance.88 Side reactions and the associated intermediates

can degrade fuel cell components such as membranes and electrodes, thereby reducing the

lifetime, one of the crucial issues in the commercialization of fuel cells.146 The influence

of side reactions and reaction intermediates on the impedance response is comparatively

unexplored.









LIST OF SYMBOLS

bi Tafel constant (inversely related to the Tafel slope), V-l

c concentration, mole/cm3

Co double 1 on ri_ capacitance, p~F/cm2

Di I;T d -iffui-;rii of i species in ionomer ..... 1.1.. 1~! i Iles of the catalyst 1... r, m2 S

i current density, mA/cm2

K(3 rtie COnStant, mol/s

KH ate COnStant of hydrogen oxidation, A cm/mol

KHzOz Tate COnStant of peroxide formation, A/mol

K~o, rate constant of oxygen reduction, A cm/mol

K~pt rate constant of Pt oxidation, A cm/mol

K(Pt,b backward rate constant of Pt oxidation, A/cm2

Kpt~f forward rate constant of Pt oxidation, A/mol

KPto rate constant of PtO formation, A cm/mol

n number of electron exchanged in the reaction

Re membrane resistance, Ocm2

t current density, mA/cm2

U cell potential, V

Zj imaginary part of impedance, Ocm2

Z, real part of impedance, O~cm2

6 diffusion 1 ... r film thickness, m

Maximum surface concentration, mole/cm2

y fractional surface concentration, dimensionless

rli overpotential, V

co frequency, s-l










2.4 Electrochemical Impedance Spectroscopy

Impedance spectroscopy is a very useful diagnostic tool because it is a non-invasive

technique and can procure information about the processes inside the fuel cell. It is a

powerful characterization technique which allows separating different processes occurring

in the system depending on time constant of the process and could be used to study com-

plex system like fuel cell. Impedance spectin 13. .p"'" 64,106,107 1S Oftell used to characterize

processes in fuel cells. The impedance study has been reported to characterize solid oxide

fuels cells (SOFCs)losals and also to characterize methanol fuel cellS.114,115 An extensive

impedance investigation for PEMFCs has been reported in literature.

Springer et
two are, a high frequency are reflecting the combination of an effective charge transfer

resistance and a double- lai-< v capacitance in the catalyst 11s-c v and a low-frequency are

reflecting mass-transport limitations within the backing 11s-c r. Cirreanu et al.1or have

conducted rigorous kinetics study for the fuel cell by the impedance techniques. Merida

et
fuel-cell diagnostics. Lee et al.6o used impedance to evaluate the optimum Nafion loading

in the catalyst active l u-; c (CAL). Song et
composition of the catalyst 111-c v support material. C'!s I et
micro flow channel. Effects of repetitive freezing of water residing in PEMFC, on the

characteristics of the fuel cell were investigated by Cho.""s Some research groupS119-123

have also used the impedance to characterize CO tolerance of the fuel cell. A descriptive

review of literature related to impedance investigations of various aspects of the fuel cell is

presented in (I Ilpter 3

Application of this technique to fuel cells has been hampered because the experiments

are difficult to perform and are prone to artifacts, and fundamental interpretation models

are not available. The fuel cells are sensitive to anything inside the cell, so it is difficult to

determine if data from instrumentation inside the cell is due to cell behavior or due to the











2.5 er -I
r~~" 1.0-
2.0 -ooo

m 1.5 -o 0.5 O Experimentalda O IIO
E o E -Model 2 O O
o a ~- Model 3 O O
C: 1.0C .1 -1 .
SO Experimental data O
N -Model 2 O_ N 00 ,
0.5C -Model 3

0.0-
a l e l a i n I ~-0.5 mlal
10*5 10-3 10 1 103 10*5 10-3 10 1 103
flHz fl Hz

(a) (b)

Figure 5-14: Impedance response for 0.3 A/cm2 generated by Models 2 and 3 for 40 oC us-
ing parameters reported in Table 5-1: a) real part of the impedance of the model response
compared with the experimental data presented in Figure 5-3(b), and b) imaginary part of
the impedance of the model response compared with the experimental data presented in
Figure 5-3(b).


and 3 were found to be capable of yielding low-frequency inductive loops at all portions of

the polarization curve.

5.6 Discussion

The inductive loops seen in low-frequency impedance measurements for the fuel cell

have gained recent attention in the literature. Several explanations have been proposed.

Models for impedance response are not unique, and many models can lead to specific

features such as the low-frequency inductive loops described in the present work. The

influence of carbon monoxide poisoning on the anode kinetics has been invoked by several

authorS.106, 119, 187, 122 The cathode kinetics were limiting in the configuration emploi-v I

in the present experiments, which used a symmetric platinum loading. In addition, the

anode and cathode gases used were rated ultra-pure, so the influence of carbon monoxide

could be excluded for the present experiments. Wiezell et al.145,217 have proposed that

non-uniform water transport in the anode could lead to low-frequency inductive loops due

to the influence of water on the anode kinetics. Such an explanation does not apply for

the present experiments as they were dominated by cathode kinetics.










for hydrogen and air was 1.5 and 2.5, respectively, and the cell was operated at the

fully-humidified condition.

6.2.2 Electrochemical Impedance Measurements

Impedance measurements were performed with the 850C fuel-cell test station, which

contains an electronic load and impedance measurement capability. All electrochemical

measurements were performed with a two-electrode cell. The anode was used as a pseudo-

reference electrode. The impedance measurements were conducted in galvanostatic

mode for a frequency range of 10 kHz to 5 mHz with a 10 mA peak-to-peak sinusoidal

perturbation. The corresponding potential perturbation ranged from 0.04 mV to 0.4 mV.

The perturbation amplitude selected was the largest amplitude that did not cause visible

distortions in low-frequency L;i .Lans plots. The frequencies were spaced in logarithmic

progression with 10 points per frequency decade. Impedance scans were conducted in

auto-integration mode with a minimum of 2 cycles per frequency measured.

6.2.3 Aging Protocol for the Samples

The fresh sample was analyzed as received from the vendor. The aged sample was

used in the fuel cell for a period of 3 months operating at various steady current loads for

9 hours/d~i- of a total period of 600 hours.

6.2.4 Surface Analysis

Several microstructural characterizations techniques were emploi- II to study the

morphology, sintering, and oxidation state of elements in the cathode catalyst lai;. r of the

MEA.

6.2.4.1 Scanning electron microscope

For sample preparation, a small portion from the center of the both fresh and used

MEA was cut with sharp razor and the SEM images were taken with the JOEL JSM 6400

available at MAIC in the University of Florida.









The steady-state surface coverage of the platinum oxide is given as

K~pt,f bet,f exp(bpt,trlpt,f)
7PO KPt,bbpt,f exp(bpt,tr7Pt,f) + KPt,bbPt,b exp(-bPt,briPt~b) + 2FK3 (-2

Model 3 was derived for a general expression of Ken as described in equation (5-42) but

for KPto << KPt, the expression for Ken reduces to


Kenf = Kpt (1 7Pto) (5-53)


which simplifies equation(5-46) to

1 1 1 1 1
Ap~ = +~ b (5-54)

and equation (5-45) to


Rt~oz = [Kipt (1 7880O)F03 (0) bo% exp (-boal 902)] (5-55)

Expressions for Rt,Hz and ZD,Hz Were giVen by equations (5-22) and (5-23), respectively,
as defined in Model 1.

The impedance response for Model 3 can be expressed as the equivalent circuit shown

in Figure 5-2(a) for the anode and Figure 5-2(d) for the cathode. The term Ze in Figure

5-1 is given by

Zeo = +p, (5-56)

As was discussed for Model 2, the surface coverage of PtO influences the impedance

contributions of Zo, and Zpt.

5.5 Results

The experimental results of the steady-state and impedance measurements are

discussed in this section and compared to the impedance response generated by the three

mechanistic models discussed in previous sections.










stochastic errors in the impedance increased with increasing current density, in particular

for the lower frequencies of 0.1 and 10 Hz. The standard deviation at lower frequencies are

higher than that at higher frequencies for any given current density.

The statistical nature of the error structure may be used to explain the larger

standard deviation observed at larger current densities. As shown in Figure 7-4(b),

the standard deviation of the real part of the impedance at 1 Hz was much higher as

compared to imaginary part. The results presented in Figure 7-4(a) indicate that at

100 Hz, the standard deviation of real and imaginary parts of the impedance were also

unequal, but the imaginary part of the impedance seems to have the larger standard

deviation. For causal systems which satisfy the K~ramers-K~ronig relations, the standard

deviation in the real and imaginary parts should be equal.223 The literature indicates

that, at low frequencies, the real part of the impedance is more sensitive to flooding,12, 116

therefore, the higher standard deviation of the real part of the impedance observed at low

frequencies may be attributed to onset of flooding.

7.2.2.2 Baseline error structure

To establish a baseline error-structure model for the standard deviation of impedance

measurements in the absence of flooding, a measurement model analysiS124, 125, 221, 194 WaS

applied to a large set of replicated impedance data. The measurement model was used

to filter small systematic changes from one measurement to the other. The standard

deviations for impedance response recorded at 0.4 A/cm2, preSented in Figure 7-6, were

smaller than those observed at both larger and at smaller current densities. The real and

imaginary parts of the impedance were statistically indistinguishable at all frequencies,

in agreement with expectations for data that are consistent with the K~ramers-K~ronigf

relations.

The model for error structure developed in previous work for a broad variety of

electrochemical and electronic systemS135,210 did not provide a good representation of

the error structure presented in Figure 7-6. The failure of the general model to apply










the perfluorinated ionomeric membrane with an ionic liquid to improve its high temper-

ature stability.27 To improve the hydration characteristics of Nafion, nanoparticles of

hygroscopic metal oxides such as Silicon oxide is incorporated into Nafion. The water

retention capacity is improves which enable use of this composite at elevated temperature

however, the composite shows higher ohmic resistance may be due to disruption of proton

conduction path in Nafion by presence of silicon oxide particles.20

Non-Nafion membranes were also investigated for intermediate-temp erature oper-

ation of fuel Cells.28, 29 Usually, phosphate based proton conductors are blended with

inorganic compound such as silicate or metal which provide mechanical stability to the

composite. Since PO, is thermally stable above 200 oC while proton sources (S0,2)

in Nafion decomposes above 200 oC. Several composite membranes for high tempera-

ture applications"so-:3 are investigated. Composite membrane were explored by doping

Nafion with different heteropolyacids such as phosphotungstic acid, silicotungstic acid,

phosphomolybdic acid, and silicomolybdic acid.:32 He', q n .k Iislle typically exist in the

hydrated phase with 30 to 6 water molecules per acid molecule; the rationale behind using

these acids is to utilize the additional water molecule for humidification of membrane

especially at higher temperature. Very little improvement in the performance is recorded

which is attributed to larger particles of these additives which are unable to help con-

duction of protons through the membrane cluster. It is also reported that these acids

dissolve; 1\olybdate atoms are observed on catalyst l~i-;r which may be due to migration

of molecules to catalyst l~i-;r though additives with Tungsten is relatively stable in the

membrane. To improve above disadvantages, these acids are stabilized by cations which

ensure uniform dispersion of smaller acid particles and therefore help create effective

bridging between ionic domains.:32

Heterocyclic aromatic polymer are used due to their excellent thermal and chemical

resistance and superior mechanical integrity. Some of the most promising candidates for

proton-exchange membranes are high performance polymers, ie. polyimides, poly(ether











-0.005


-0.004-


-0.003 o


0 -0.002-*
-0.010 -I C
*Inconsistent data
N -0.001-


C: -0.005 A -I 0


0.001-
0.000*
0.002
0.002 0.021 0.022 0.023 0.024
102 103 104
fI Hz Z / 0 cm2

(a) (b)

Figure 4-7: Detailed representation of impedance data showing the inconsistency observed
at high frequency: a) expanded view of Figure 4-5(b), b) expanded view of a Nyquist rep-
resentation (see Figure 4-3 for a complete spectrum). The filled symbols correspond to
data that were deemed inconsistent with the K~ramers-K~ronigf relations.


A similar analysis was performed for the first and second measurements obtained

by both the FC350 and the 850C instruments. For all measurements, data measured

at frequencies above 1000 Hz were found to be inconsistent with the K~ramers-K~ronig

relations. These data were removed from the data used in subsequent regressions.

It is important to note that removal of data for which the imaginary impedance had

a positive value was not sufficient to eliminate inconsistency with the K~ramers-K~ronig

relations. As shown in Figure 4-7(a), the influence of the artifact extended well into the

domain in which the imaginary impedance had a negative value. The filled symbols in

Figure 4-7(a) correspond to data that were deemed inconsistent with the K~ramers-K~ronig

relations. The result may be seen as well in the Nyquist plot given as Figure 4-7(b).









2.3.2 Platinum Oxidation and Dissolution

Platinum dissolves'o in the fuel cell environment, which can also leads to the loss

of catalytic activity and, consequently, the degradation of the electrode of the fuel cell

and hence loss in performance.88 A scheme for dissolution of platinum was -II_a-r-- -1. by

?1, i-n rs et al.1o as follows.


Pt + H20 0 PtO + 2H+ + 2e- (2-13)


in which PtO is formed, followed by a chemical dissolution reaction


PtO + 2H+ Pt+2 + H20 (2-14)


The first step leads to formation of a protective 1 e. -r of PtO which reduces active surface

area by blocking reaction sites. In the second step, the PtO oxide dissolves to form Pt

ion leading to loss of catalyst particles. The formation of the platinum oxide is supposed

to have an indirect influence on the ORR at the cathode by changing the effective rate

constant for the reaction.

Another scheme for PtO formation in presence of water/oxygen was advocated along

with different reactive radicals which degrade membrane, catalyst, and catalyst support

used in the fuel cell.89 Effect of humidity on PtO formation was reported, formation of

PtO was observed even in absence of oxygen at the cathode.90 The oxide formation was

proposed to follow

Pt + H20 Pt OH + H+ + e- (2-15)

Pt OH PtO + H+ + e- (2-16)

with a larger amount of PtO observed at lower humidity.

The formation of PtO, and PtO2 WaS reported to follow.91


Pt + H20 PtO + 2H+ + 2e- (2-17)










of low-frequency data with the K~ramers-K~ronig relations. These data were collected

approximately after 3 hours of cell operation at the specified current.

The established start-up procedures,192 including stabilization of potential at a set

current, were not sufficient to ensure the steady-state condition. Impedance spectroscopy

is seen to be much more sensitive to the condition of the fuel cell. This work demonstrates

the utility of the measurement-model error an~ ll--- for identifying steady-state operation.

Not all low-frequency inductive loops were free of artifacts caused by nonstationary

behavior, but, once a steady-state operation was established, the low-frequency inductive

loops were found to be consistent with the K~ramers-K~ronig relations. The low-frequency

inductive loops in the fuel cell can therefore he attributed to the response of physical

processes occurring within the fuel cell.










7.3 Discussion

Due to its influence on mass transfer and kinetics, the onset of floodingf in the fuel cell

can he identified by a decrease in cell potential at fixed current or a decrease in current

at fixed potential. Similarly, the onset of flooding can he identified by an increase in the

cell impedance. In the present work, the increase in the low-frequency cell impedance

associated with floodingf was on the order of 10 percent. The increase of 10 percent in the

cell impedance was accompanied by an increase in the standard deviation of the real part

of the impedance by 2000 or 3000 percent.

The increase in stochastic errors in the impedance measurement can he attributed to

the random character of the floodingf process in which droplets of water are formed and

then removed by gas flow. In fact, the increase in stochastic errors provides verification

that the increased cell impedance was at least partially due to flooding. Impedance

spectroscopy has been shown to provide a more sensitive assessment of cell condition

than steady-state measurements of cell potential and current. The difficulty with using

impedance directly to detect flooding is that a baseline value for the impedance must he

established in the absence of floodingf. This baseline must, however, change with time due

to systematic changes to catalyst and nientrane properties that are not associated with

flooding. Thus, a baseline established when a cell is first coninissioned will not he valid

throughout the lifetime of the cell.

In contrast, the model given by equation (7-1) for the standard deviation of the

impedance should be affected largely by instrumental settings, and, so long as the

impedance is measured in the same way, a baseline established for the standard devia-

tion of impedance measurements in the flooded condition should be valid throughout the

lifetime of the cell. In addition, the change in the standard deviation of the measurement

caused by flooding is 100 times larger than the corresponding change in the value of the

impedance. Thus, assessment of the standard deviation of impedance measurements will

provide a more sensitive indicator for the onset of floodingf in a PE1\ fuel cell.










2.4.3 Flooding in the Fuel Cell

The performance of the fuel cell is influenced by kinetic limitations at low current

densities, Ohmic limitations at intermediate current densities, and mass-transfer limita-

tions at high current densities. K(ulikovskyl47 and Berg et al.148 have described in detail

the critical role of water management in operation of the fuel cell. To maintain proton

conductivity, the fuel cell membrane must remain hydrated. To achieve hydration, the

relative humidity of inlet gasses is typically held at a large value. Water, however, is also

a product of the cathodic reaction; thus, an excess of water in the cathode is commonly

observed, which can lead to condensation and subsequent flooding. Flooding increases the

resistance associated with the gas diffusion 111-< v and may even block flow channels, re-

ducing the availability of oxygen.149 Condensed water may be removed by gas flow. Thus,

changes in design of reactant flow channels and gas diffusion l~i-;-rs have been proposed to

reduce the influence of flooding.

Pressure drop has been reported to provide a suitable diagnostic tool for monitoring

flooding in the fuel cell.15o Flooding was also investigated by correlating the appearance

of floodingf to the Faradaic resistance.l51 Barbir et al.152 have investigated the relationship

between pressure drop and cell resistance to make a distinction between floodingf and

drying. They observed that both pressure drop and cell resistance changed in case of

drying; whereas, only pressure drop changed under flooding conditions. Ge et
observed that the anode flooding is mainly due to water-droplet condensation at channel

walls in contrast to flooding at the cathode which is usually attributed to condensation

in gas diffusion 1e. ;r (GDL). They have also reported that use of a hydrophilic GDL and

elevated anode plate temperature could mitigate anode floodingf. The onset of floodingf

may be seen in steady-state measurements, but the impedance response is even more

sensitive to appearance of flooding conditions. The impedance technique has recently

been used to detect membrane drying, flooding, and anode poisoning of fuel cell stackS.12

1\erida et








USE OF IMPEDANCE SPECTROSCOPY TO INVESTIGATE FACTORS THAT
INFLUENCE THE PERFORMANCE AND DURABILITY OF PROTON EXCHANGE
MEMBRANE (PEM) FUEL CELLS


















By
SUNIL K(. ROY


A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE DEGREE OF
DOCTOR OF PHILOSOPHY

UNIVERSITY OF FLORIDA

2008









Table 5-1: Parameters used to calculate the impedance response corresponding to Models
1, 2, and 3.
Parameters Model 1 Model 2 Model 3
Do, m2 S 4 x10-11 4 x10-11 4 x10-11
DH m2 S 4 x10-9 4 x10-9 4 x10-9
DHzOz m2/S 4 x 10-1s
5, m 1 x10-6 1 x10-6 1 x10-6
Re, O~cm2 0.135 0.135 0.135
C'o, F 0.212 0.212 0.212
bH? V-l 65 40 40
bO2, V- 1 27 27 45
bHzOz V-l 15
bpt, V-l 14
K(Hz, Acm/mol 0.55 1.34 1.35
Kos Am/ol 961.9 10900 10900
KHzOz, A/mol 1900
Kpt, Acm/mol 6.2
KPto, Acm/moll 0.01
K3, mol/S 0.01
KPt,f A/mol 0.01
K(Pt,b, A/cm2 0.01


the previous sections. These models were compared to the experimental polarization

and impedance data. The method emploi-. 4 was to calculate the polarization curve that

matched closely the experimental results and then to use the same parameters to estimate

the impedance response at different currents. Direct regression was not emploi-. 4 as the

model does not account explicitly for the non-uniform reaction rates along the length of

the serpentine flow channels.

Model parameters are presented in Table 5-1. Constant values were assumed for the

interfacial capacitance, ionic resistance in the catalyst 1... r, membrane resistance, and

oxygen permeability through ionomer ..z.In,_~~~! I .Les in the catalyst 1... -r. When appro-

priate, numerical values were taken from the literature.64 The impedance response for all

simulations corresponded to a frequency range of 10 kHz to 0.001 mHz. Calculations at

low frequency were used to explore more fully the low-frequency inductive features.










Small angle X-ray scattering and neutron scattering experiments can be used to indicate

ionic clustering in Nafion.

The proton conductivity of Nafion is dependant on its hydration state. In the dry

state, Nafion is a poor ion conductor, but ionic conductivity increases sharply with

water content.3 In dry state, protons may migrate from one acid group to another in the

network; the associated activation energy is relatively high, resulting in relatively low ionic

conductivity. However, when water fills the pore network, the protons are solvated by

one or more water molecules. Water solvation partially screens the proton charge, thus

lowering the activation energy for migration. To ensure membrane hydration humidified

gases are generally fed into the fuel cell.

Nafion dehydrates at temperature above 800C; the dehydration can cause membrane

to shrink, reducing contact between electrodes and membrane therefore higher contact

resistance. The shrink may also cause pinholes formation, leading to reactant crossover.20

Nafion also shows considerable deterioration in the conductivity and the mechanical

strength above the glass transition temperature (ca. 1100C).

A lifetime of over 60,000 hours under fuel cell conditions has been achieved with

commercial Nafion membranes. However, even extremely stable Nafion can suffer from

degradation. Using XPS analysis of the MEA before and after fuel cell operation Huang

et al.21 has found that -CF2- groups of Nafion are destroyed under electrochemical

stress, yielding the -HCF- or -CCF- configurations. Under the anode potential, the

hydrophobic part (e.g., fluorocarbon) may react with carbon or hydrogen atoms, resulting

finally in the degradation of the electrolyte. Also, this kind of hydrocarbon membranes

are prone to oxidative degradation by peroxide intermediates. The high cost and high

methanol permeability of the fluorinated polymers also urge the necessity to develop

alternative proton-conducting polymers.










___________


0.10 Hz,/
S15 '



10 P

0 1Hz -


::-s- 100 Hz..--a
0-- --

0.4 0.6 0.8 1.0 1.2 1.4

Current Density / A cm-2

Figure 7-11: Normalized standard deviations for the real part of the impedance calculated
from the data shown in Figure 7-3 as a function of current density with frequency as a
parameter.


1.4 A/cm2 are clearly larger than that predicted by equation (7-1). The discrepancy may

be attributed to stochastic processes within the cell such as associated with flooding.

The standard deviations presented in Figure 7-5 were normalized by the base-

stochastic errors level calculated using the error structure presented by equation (7-1).

The result for the real part of the impedance is presented in Figure 7-11. As shown in

Figure 7-11, the standard deviation of the impedance data increased with an increase in

the operating current. The increased noise levels are seen at a frequency of 100 Hz as well

as at lower frequencies. At large current densities and at low frequencies, the standard

deviation calculated for the real part of the impedance was more than 20 times that

obtained in the absence of flooding. The standard deviation of the imaginary part of the

impedance had no clear dependency on flooding. The standard deviation of the real part

particularly at low frequency, however, can he used to detect onset of flooding.










An optimal film thickness for given Nafionn loading was so-----~ -1. .1 60 A Nafion

loading of 1.3 mg/cm2 WaS found to correspond to the optimal film thickness sufficient

to transport proton without hindering electron and gas transport. Nafion loading greater

than the optimal value results in an additional arc at low frequency in impedance response

representing gas-diffusion limitation.61 Further improvement in Nafion loading is obtained

to 0.8 mg/cm2 by using a catalyst support between catalyst 111-;-r and gas diffusion 111-- r

in the fuel cell.61 Electrodes consisting of two 111-;- rs with different Nafion loading was also

proposed, but no better performance was obtained.62

2.2.3 Gas Diffusion Layers

The functions of the gas diffusion 111-;- rs are to provide structural support for the

catalyst 1...r-is, passages for reactant gases to reach the catalyst 1...r-is and transport of

water to or from the < Ir 11i--i 17 r~-;s, electron transport from the catalyst lIn-;-r to the

bipolar plate in the anode side and from the bipolar plate to the catalyst 1... -r in the

cathode side, and heat removal from the catalyst lI-;-ir;. The common materials for the

GDL are carbon paper and carbon cloth which incorporates a hydrophobic material,

such as PTFE to prevent water from pooling within the pore of the backing lI l...r

Furthermore, PTFE creates a non-wetting surface within the passages of the backing

material which facilitates product water removal on the cathode.

The physical properties such as pore size and structure, hydrophobicity, and thickness

of GDL pIIlai- in .jur role in mass-transport processes. K~ong et al.63 report that macro-

pores prevent flooding and thus improves performance. To modify pore structure, pore-

formingf agents such as Li2CO3 WeTO illVeStigated. Some authorS64-66 -11***** -( II us ing

a two-lIn-;-r structure as a gas backing. The 1... -r closer to the electrode is know as

the diffusion 111-;- rs and should have a finer structure to ensure that as many catalyst

particles as possible are in electric contact. Capillary action associated with the finer

pore structure enhance transport of reactants to the catalyst sites. The diffusion 111-- r

distributes reactants more uniformly, enhances mechanical compatibly with catalyst 1 ... r,










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[140] T. E. Springer and I. D. Raistrick, "Electrical Impedance of Pore Wall for the
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[141] F. Jaouen and G. Lindberg, "Transient Techniques for Investigating Mass Transport
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[142] Q. Guo, M. C ?i-; tano, Y. Tsou, E. S. D. Castro, and R. E. White, "Study of
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[143] H. F. Oetjen, V. M. Schmidt, U. Stimming, and F. Trila, "Performance Data of a
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I


E 0.25 0 Experimental data O O
E -Model2
C:o Model 3
SO Experimental data a
N0.5 -Model2N O
Model 3
0.00 -- .

0.0 llal
10*5 10-3 10 1 103 5311 a I
10 5 1010 10' 103
fl Hz
fl Hz

(a) (b)


Figure 5-10: Impedance response for 0.05 A/cm2 generated by Models 2 and :3 for 40
o"C using parameters reported in Table 5-1: a) real part of the impedance of the model
response compared with the experimental data presented in Figure 5-:3(b); and b) imagi-
nary part of the impedance of the model response compared with the experimental data
presented in Figure 5-:3(b).


T\TT\


N 0.25
E
o
C:

I


Z / cm2


Figure 5-11: Impedance response for 0.2 A/cm2 generated by Models 2 and :3 for 40 oC' us-
ing parameters reported in Table 5-1 and compared with the experimental data presented
in Figure 5-:3(b).


O OO
O

o O Experimental data
oo model 2
*Model 3










5-6 Impedance response for 0.2 A/eni2 generate(1 by Model 1 for 40 o"C using pa-
ranleters reported in Table 5-1; a) real part of the impedance of the model re-
sponse compared with the experimental data presented in the Figure 5-:3(b);
and b) imaginary part of the impedance of the model response compared with
the experimental data presented in Figure 5-:3(b). ... ... .. 105

5-7 Polarization curve generated by Models 2 and :3 for 40 o"C using parameters re-
ported in Table 5-1 and compared with the experimental data presented in Figf-
ure 5-:3(a). ............ ........... 106

5-8 Relative contributions of two reactions to total current at the cathode: a) Model
2; and b) Model :3. ......... . .. 107

5-9 Impedance response for 0.05 A/eni2 generated by Models 2 and :3 for 40 oC' us-
ing parameters reported in Table 5-1 and compared with the experimental data
presented in Figure 5-:3(b). ......... .. .. 107

5-10 Impedance response for 0.05 A/eni2 generated by Models 2 and :3 for 40 oC' us-
ing parameters reported in Table 5-1: a) real part of the impedance of the model
response compared with the experimental data presented in Figure 5-:3(b); and
b) imaginary part of the impedance of the model response compared with the
experimental data presented in Figure 5-:3(b). .... ... .. 108

5-11 Impedance response for 0.2 A/eni2 generated by Models 2 and :3 for 40 oC' us-
ing parameters reported in Table 5-1 and compared with the experimental data
presented in Figure 5-:3(b). ......... .. .. 108

5-12 Impedance response for 0.2 A/eni2 generated by Models 2 and :3 for 40 oC' us-
ing parameters reported in Table 5-1: a) real part of the impedance of the model
response compared with the experimental data presented in Figure 5-:3(b); and
b) imaginary part of the impedance of the model response compared with the
experimental data presented in Figure 5-:3(b). .... ... .. 109

5-1:3 Impedance response for 0.3 A/eni2 generated by Models 2 and :3 for 40 oC' us-
ing parameters reported in Table 5-1 and compared with the experimental data
presented in Figure 5-:3(b). ......... .. .. 109

5-14 Impedance response for 0.3 A/eni2 generated by Models 2 and :3 for 40 oC' us-
ing parameters reported in Table 5-1: a) real part of the impedance of the model
response compared with the experimental data presented in Figure 5-:3(b); and
b) imaginary part of the impedance of the model response compared with the
experimental data presented in Figure 5-:3(b). .... ... .. 110

5-15 Fractional surface-coverage of the intermediates plotted a) as a function of cell
potential; and b) as a function of current density. ... ... .. 111




Full Text

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USEOFIMPEDANCESPECTROSCOPYTOINVESTIGATEFACTORSTHAT INFLUENCETHEPERFORMANCEANDDURABILITYOFPROTONEXCHANGE MEMBRANEPEMFUELCELLS By SUNILK.ROY ADISSERTATIONPRESENTEDTOTHEGRADUATESCHOOL OFTHEUNIVERSITYOFFLORIDAINPARTIALFULFILLMENT OFTHEREQUIREMENTSFORTHEDEGREEOF DOCTOROFPHILOSOPHY UNIVERSITYOFFLORIDA 2008 1

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c 2008SunilK.Roy 2

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Tomemoryofmylatemotherandsiblings Toinspirationandsacriceofmyfather Todedicationofmysister-in-law Tosmileofmyangels,MayankandJayant TomywifeAsmita,thebestgiftIhavereceivedfromGOD. 3

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ACKNOWLEDGMENTS Ithankmyadvisor,ProfessorMarkOrazem,forhissupport,andguidance.Hehas shownmenotonlyhowtoimprovemyabilitiesinresearch,butalsohowtoimprovemy abilitiesasaperson. Iwishtothankmycolleagues,andgroupmemberPatrickMcKinney,ErinPatrick, Shao-lingWu,andBryanHirschorn,fortheirsupportandencouragementoverthepast fouryears.Wehaveenjoyedconversationonthephilosophyoflifeaswellasonthe technicalissuesassociatedwithelectrochemistry.Bylisteningtomytalksmanytimes, theyhavehelpedmeimprovemypresentationskills.IthankChemicalEngineeringstas ShirleyKelly,DennisVince,JamesHinnant,SeanPoole,andDeborahAldrichfortheir helpwithtechnical,computer,andpurchase,respectively,essentialformyresearch. IwouldalsoliketothankNASAandGamryInstrumentsInc.forsupportingthis work.ThisworkwassupportedbyNASAGlennResearchCenterundergrantNAG 3-2930monitoredbyTimothySmithwithadditionalsupportfromGamryInstruments Inc. Finally,Iliketogivespecialcredittomyparents,mysister,andmybrotherfortheir loveandsupportthroughoutmylife. 4

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TABLEOFCONTENTS page ACKNOWLEDGMENTS.................................4 LISTOFTABLES.....................................8 LISTOFFIGURES....................................9 LISTOFSYMBOLS ABSTRACT........................................19 1INTRODUCTION..................................21 2LITERATUREREVIEW..............................22 2.1ElectrochemistryandLossesintheFuelCell.................23 2.1.1ActivationLoss.............................25 2.1.2OhmicPotentialLoss..........................26 2.1.3ConcentrationOverpotentialLoss...................26 2.1.4ParasiticPotentialLoss.........................27 2.2PEMFuelCellComponents..........................28 2.2.1Membrane................................28 2.2.2Electrodes................................32 2.2.3GasDiusionLayers..........................36 2.2.4BipolarPlates..............................37 2.3DegradationMechanismsinFuelCells....................39 2.3.1HydrogenPeroxideFormation.....................39 2.3.2PlatinumOxidationandDissolution..................41 2.4ElectrochemicalImpedanceSpectroscopy...................44 2.4.1MeasurementModelAnalysis.....................45 2.4.2InterpretationModel..........................47 2.4.3FloodingintheFuelCell........................49 2.4.4EvaluationofInterfacialCapacitance.................50 3EXPERIMENTAL..................................52 3.1Introduction...................................52 3.2Experimental..................................56 3.2.1MaterialsandChemicals........................56 3.2.2ElectrochemicalImpedanceMeasurements..............58 3.2.3OtherElectrochemicalTechniques...................59 3.2.4SurfaceAnalysis.............................59 3.2.4.1Scanningelectronmicroscope................60 3.2.4.2Transmissionelectronmicroscope..............60 3.2.4.3X-rayphotoelectronspectroscopy..............60 3.3Results......................................61 5

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3.3.1CurrentDensityasaParameter....................61 3.3.2TemperatureasaParameter......................62 3.3.3BackpressureasaParameter......................62 3.3.4HysteresisBehaviorandImpedanceResponse............65 3.3.5TimeasaParameter..........................66 3.3.6FlowChannelasaParameter.....................69 4ERRORANALYSISOFIMPEDANCERESPONSE...............74 4.1Introduction...................................74 4.2Results......................................76 4.2.1EvaluationofStochasticErrors....................76 4.2.2EvaluationofHigh-FrequencyBiasErrors...............78 4.2.3EvaluationofLow-FrequencyBiasErrors...............82 4.2.4ImpedanceResponseafterErrorAnalysis...............85 4.3Discussion....................................87 5INTERPRETATIONOFIMPEDANCERESPONSE...............89 5.1Introduction...................................89 5.2ClassofModelDevelopment..........................89 5.3ModelFramework................................90 5.3.1PolarizationCurve...........................90 5.3.2ImpedanceResponse..........................91 5.4ImpedanceResponseforProposedReactionMechanisms..........92 5.4.1Model1:SimpleReactionKinetics..................93 5.4.2Model2:HydrogenPeroxideFormation................95 5.4.3Model3:PlatinumDissolution.....................99 5.5Results......................................101 5.5.1ExperimentalPolarizationandImpedanceResults..........102 5.5.2ModelResponseAnalysis........................102 5.5.2.1Model1............................104 5.5.2.2Models2and3........................106 5.6Discussion....................................110 6RESULTSOFEX-SITUANALYSIS........................113 6.1Introduction..................................113 6.2Experimental..................................114 6.2.1MaterialsandChemicals........................114 6.2.2ElectrochemicalImpedanceMeasurements..............115 6.2.3AgingProtocolfortheSamples....................115 6.2.4SurfaceAnalysis.............................115 6.2.4.1Scanningelectronmicroscope................115 6.2.4.2Transmissionelectronmicroscope..............116 6.2.4.3X-rayphotoelectronspectroscopy..............116 6.3Results.....................................116 6

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6.3.1MicrostructuralCharacterization...................117 6.3.2EuentAnalysis............................120 6.3.3ElectrochemicalResponse........................121 7DETECTIONOFONSETOFFLOODING....................124 7.1Introduction...................................124 7.2Results......................................124 7.2.1ImpedanceResponse..........................124 7.2.2StochasticErrorinImpedanceResponse...............126 7.2.2.1Sensitivitytoooding....................126 7.2.2.2Baselineerrorstructure...................128 7.2.2.3Detectionofoodedconditions...............131 7.2.2.4Detectionofdryconditions.................134 7.3Discussion...................................136 8EVALUATIONOFINTERFACIALCAPACITANCE...............138 8.1Introduction...................................138 8.2Results......................................138 8.2.1ApplicationofAsymptoticGraphicalAnalysis............139 8.2.2EectofOperatingParameters....................143 8.2.3EectofDesignParameters......................145 8.2.4TransientBehavior...........................146 8.3Discussion....................................147 9CONCLUSIONS...................................150 9.1ErrorAnalysisofImpedanceResponse....................150 9.2InterpretationofImpedanceResponse....................150 9.3Ex-SituAnalysis................................151 9.4DetectingOnsetofFlooding..........................151 9.5EvaluationofInterfacialCapacitance.....................152 10FUTUREDIRECTIONS...............................153 10.1ParameterEvaluation..............................153 10.2Euent,andMicrostructureAnalysis.....................153 10.3One-DimensionalFlowChannel........................153 APPENDIXA:COMPUTATIONALALGORITHMFORMODEL1........154 APPENDIXB:COMPUTATIONALALGORITHMFORMODEL2........157 APPENDIXC:COMPUTATIONALALGORITHMFORMODEL3........159 REFERENCES.......................................161 BIOGRAPHICALSKETCH................................180 7

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LISTOFTABLES Table page 5-1ParametersusedtocalculatetheimpedanceresponsecorrespondingtoModels 1,2,and3.......................................103 8

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LISTOFFIGURES Figure page 2-1Illustrationofthefuelcelltakenfromliterature 1 ;aowdiagram;andbcomponents.........................................24 2-2ApolarizationcurveforafuelcelltakenfromLin etal. 2 ,showingthelosses associatedwithreactionkinetics,internalelectricalresistance,andmasstransports..........................................25 2-3ChemicalstructureofNaontakenfromWeberandNewman etal. 3 ......28 2-4AschematicrepresentationofmembraneelectrodeassemblyMEAtakenfrom literature 1 .......................................33 3-1Thecongurationsofowchannels; 4 aserpentine;andbinterdigitated.....57 3-2Polarizationcurvesrecordedwiththe850Cforaninterdigitatedchannelasa functionofcurrentdensitiesatthecelltemperature40 C.Theanodeandthe celltemperaturesweresetat40 Candthecathodetemperatureat35 C....61 3-3Impedanceresponsescollectedwiththe850Cforaninterdigitatedchannelasa functionofcurrentdensitiesatthecelltemperature40 C.Theanodeandthe celltemperaturesweresetat40 Candthecathodetemperatureat35 C....62 3-4Polarizationcurvesrecordedasafunctionofcelltemperaturebythesteadystate measurementwiththe850CforH 2 asreactantattheanodeandairasoxidant atthecathode.Theanodethecathodetemperatureatwerexedat70 C.The fuelcellwasassembledwithaserpentinechannel..................63 3-5Impedanceresponsesasafunctionoftemperatureat0.5A/cm 2 collectedwith the850Cwithaserpentinechannel..........................63 3-6Cellperformanceasafunctionofbackpressure.Themeasurementswereconductedwith850CforH 2 asreactantattheanodeandairasoxidantatcathode.Theanodereactantstreamandcelltemperaturesweresetat60 0 Cand thecathodereactantstreamtemperatureat55 0 C.Thefuelcellwasassembled withaserpentinechannel;apolarizationcurvegeneratedfromthesteady-state measurement;andbimpedanceresponserecordedat0.1A/cm 2 .........64 3-7Cellperformanceasafunctionofbackpressure.Themeasurementswereconductedwith850CforH 2 asreactantattheanodeandairasoxidantatcathode.Theanodereactantstreamandcelltemperaturesweresetat60 0 Cand thecathodereactantstreamtemperatureat55 0 C.Thefuelcellwasassembled withaserpentinechannel;aimpedanceresponserecordedat0.2A/cm 2 ;and bimpedanceresponserecordedat0.4A/cm 2 ....................65 9

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3-8Galvanodynamiccurvesrecordedatacelltemperatureof40 Cusingthe850C forH 2 asreactantattheanodeandairasoxidantatthecathode:ahysteresis curveforscanrate50mA/30s;andbtheoodingregionofthehysteresiscurve.66 3-9Themeasurementrecordedwiththe850CforH 2 asreactantattheanodeand airasoxidantatthecathode.Theanode,thecathodeandcelltemperatures weresetat40 C;ahysteresiscurveforscanrate50mA/30Sec.;andbimpedance responsesasafunctionofcurrentdensities.....................67 3-10Themeasurementrecordedwiththe850CforH 2 asreactantattheanodeand airasoxidantatthecathode.Theanode,thecathodeandcelltemperatures weresetat50 C;ahysteresiscurveforscanrate50mA/30Sec.;andbimpedance responsesasafunctionofcurrentdensities.....................67 3-11Polarizationcurvegeneratedfromthesteady-statemeasurementasafunction oftimewith850CforH 2 asreactantattheanodeandairasoxidantatcathode.Theanodereactantstreamandcelltemperaturesweresetat40 0 Cand thecathodereactantstreamtemperatureat35 0 C.Thefuelcellwasassembled withaserpentineowchannel,andauniformporousGDL............68 3-12Impedanceresponsescollectedasafunctionoftimesafunctionoftimewith 850CforH 2 asreactantattheanodeandairasoxidantatcathode.Theanodereactantstreamandcelltemperaturesweresetat40 0 Candthecathode reactantstreamtemperatureat35 0 C.Thefuelcellwasassembledwithaserpentineowchannel,andauniformporousGDL..................68 3-13Thecongurationofthepostowchannel......................70 3-14Polarizationcurvesgeneratedfortwoowchannelsfromthesteady-statemeasurementwiththe850CforH 2 asreactantattheanodeandairasoxidantat thecathode.Theanodeandcelltemperaturesweresetat40 Candthecathodetemperatureat35 C.Thefuelcellwasassembledwithauniformporous GDL..........................................71 3-15Impedanceresponsescollectedwiththe850Cfortwoowchannelswiththe 850CforH 2 asreactantattheanodeandairasoxidantatthecathode.The anodeandcelltemperaturesweresetat40 Candthecathodetemperatureat 35 C.ThefuelcellwasassembledwithauniformporousGDL..........71 3-16Polarizationcurvesgeneratedforthenewandaconventionalowchannelsfrom thesteady-statemeasurementwiththe850CforH 2 asreactantattheanode andairasoxidantatthecathode.Theanodeandcelltemperaturesweresetat 40 Candthecathodetemperatureat35 C.Thefuelcellwasassembledwith auniformporousGDL.................................72 10

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3-17Impedanceresponseofthenewowchannelwith850CforH 2 asreactantat theanodeandairasoxidantatcathode.Theanodeandthecelltemperatures weresetat50 Candthecathodetemperatureat45 C.ThefuelcellwasassembledwithauniformporousGDL;aimpedanceresponsegeneratedforthe newchannelasafunctionofcurrentdensity;andbimpedanceresponserecorded at0.4A/cm 2 forthetwochannels..........................73 4-1Polarizationcurvegeneratedfromthesteady-statemeasurementwith850Cfor H 2 asreactantattheanodeandairasoxidantatcathode.Theanodereactant streamandcelltemperaturesweresetat40 0 Candthecathodereactantstream temperatureat35 0 C.................................75 4-2Theaveragetimerequiredforimpedancemeasurementateachfrequency.The errorbarsassociatedwiththestandarddeviationobtainedfromfourexperimentsissmallerthanthesymbolsusedinthegure................76 4-3Fivescansofimpedancedatacollectedatacurrentdensityof0.2A/cm 2 with theFC350.......................................77 4-4ComparisonoferrorstructuresfortheFC350lledsymbolsandthe850C. The representsthestandarddeviationoftherealpartoftheimpedance,and the 4 representstheimaginarypartoftheimpedance.Thedashedandsolid linesrepresentstheempiricalmodeloftheerrorstructuregivenbyequation 4{1.astandarddeviationsinunitsofimpedance;andbstandarddeviations normalizedbythemodulusoftheimpedance....................78 4-5RegressionoftheVoigtmodeltotherealpartoftheimpedancecorrespondingtothesecondofvescansgiveninFigure4-3:attotherealpartofthe measurement;andbpredictionoftheimaginarypart.The representstheexperimentaldata,theheavysolidlinerepresentsthemeasurementmodelt,and thethinsolidlinesrepresentcondenceintervals..................79 4-6NormalizedresidualerrorsfortheregressionpresentedinFigure4-5:atto therealpart,wheredashedlinesrepresentthe 2 boundforthestochastic error;andbpredictionoftheimaginarypart,wheresolidlinesrepresentthe 95.4%condenceintervalsforthemodelobtainedbyMonteCarlosimulations..80 4-7Detailedrepresentationofimpedancedatashowingtheinconsistencyobserved athighfrequency:aexpandedviewofFigure4-5b;bexpandedviewofa NyquistrepresentationseeFigure4-3foracompletespectrum.ThelledsymbolscorrespondtodatathatweredeemedinconsistentwiththeKramers-Kronig relations.........................................81 4-8RegressionoftheVoigtmodeltotheimaginarypartoftheimpedancecorrespondingtotherstofvescansgiveninFigure4-3:attotheimaginary partofthemeasurement;andbpredictionoftherealpart.The represents theexperimentaldata,theheavysolidlinerepresentsthemeasurementmodel t,andthethinsolidlinesrepresentcondenceintervals..............82 11

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4-9NormalizedresidualerrorsfortheregressionpresentedinFigure4-8:atto theimaginarypart,wheredashedlinesrepresentthe 2 boundforthestochasticerror;andbpredictionoftherealpart,wheresolidlinesrepresentthe95.4% condenceintervalsforthemodelobtainedbyMonteCarlosimulations......83 4-10Normalizedresidualerrorsforthetofthemeasurementmodeltothesecond scanofimpedancedatapresentedinFigure4-3:attotheimaginarypart, wheredashedlinesrepresentthe 2 boundforthestochasticerror;andb predictionoftherealpart,wheresolidlinesrepresentthe95.4%condenceintervalsforthemodelobtainedbyMonteCarlosimulations.............84 4-11RegressionoftheVoigtmodeltotheimaginarypartoftheimpedanceforthe secondscanoftheimpedancedatacollectedat0.2A/cm 2 withthe850C:at totheimaginarypartofthemeasurement;andbpredictionoftherealpart. The representsexperimentaldata,thethicksolidlinesrepresentthemeasurementmodelt,andthethinsolidlinesrepresentcondenceintervals.......85 4-12ResidualerrorsfortheregressionpresentedinFigure4-11:attotheimaginarypart,wheredashedlinesrepresentthe 2 boundforthestochasticerror; andbpredictionoftherealpart,wheresolidlinesrepresentthe95.4%condenceintervalsforthemodelobtainedbyMonteCarlosimulations........86 4-13Theresultsofcomplexregressionofthemeasurementmodeltothesecondscan oftheimpedancedatacollectedat0.2A/cm 2 withtheScribner850C.The representstheexperimentaldataandthesolidlinerepresentsthemeasurement modelt........................................86 5-1Aschematicrepresentationoftherelationshipbetweenthefuelcellgeometry andanequivalentcircuitdiagramforproposedreactionsequenceswherethe boxesrepresentFaradaicimpedancesdeterminedforspecicreactionmechanisms.93 5-2Equivalentcircuitdiagramsforproposedreactionsequenceswheretheboxes representdiusionimpedancesorFaradaicimpedancesdeterminedforspecic reactionmechanisms:aanodeforallmodels;bcathodeforModel1;ccathodeforModel2;anddcathodeforModel3....................96 5-3ElectrochemicalresultsobtainedwithH 2 asreactantattheanodeandairas oxidantatthecathode.Theanodeandcelltemperatureswere40 C,andthe cathodetemperaturewas35 C.aPolarizationcurve;andbimpedanceresponsewithcurrentdensityasaparameter.....................102 5-4PolarizationcurvegeneratedbyModel1for40 Cusingparametersreported inTable5-1andcomparedwiththeexperimentaldatapresentedinFigure5-3a.104 5-5Impedanceresponsefor0.2A/cm 2 generatedbyModel1for40 CusingparametersreportedinTable5-1andcomparedwiththeexperimentaldatapresentedinFigure5-3b................................105 12

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5-6Impedanceresponsefor0.2A/cm 2 generatedbyModel1for40 CusingparametersreportedinTable5-1;arealpartoftheimpedanceofthemodelresponsecomparedwiththeexperimentaldatapresentedintheFigure5-3b; andbimaginarypartoftheimpedanceofthemodelresponsecomparedwith theexperimentaldatapresentedinFigure5-3b..................105 5-7PolarizationcurvegeneratedbyModels2and3for40 CusingparametersreportedinTable5-1andcomparedwiththeexperimentaldatapresentedinFigure5-3a........................................106 5-8Relativecontributionsoftworeactionstototalcurrentatthecathode:aModel 2;andbModel3...................................107 5-9Impedanceresponsefor0.05A/cm 2 generatedbyModels2and3for40 CusingparametersreportedinTable5-1andcomparedwiththeexperimentaldata presentedinFigure5-3b...............................107 5-10Impedanceresponsefor0.05A/cm 2 generatedbyModels2and3for40 CusingparametersreportedinTable5-1:arealpartoftheimpedanceofthemodel responsecomparedwiththeexperimentaldatapresentedinFigure5-3b;and bimaginarypartoftheimpedanceofthemodelresponsecomparedwiththe experimentaldatapresentedinFigure5-3b....................108 5-11Impedanceresponsefor0.2A/cm 2 generatedbyModels2and3for40 CusingparametersreportedinTable5-1andcomparedwiththeexperimentaldata presentedinFigure5-3b...............................108 5-12Impedanceresponsefor0.2A/cm 2 generatedbyModels2and3for40 CusingparametersreportedinTable5-1:arealpartoftheimpedanceofthemodel responsecomparedwiththeexperimentaldatapresentedinFigure5-3b;and bimaginarypartoftheimpedanceofthemodelresponsecomparedwiththe experimentaldatapresentedinFigure5-3b....................109 5-13Impedanceresponsefor0.3A/cm 2 generatedbyModels2and3for40 CusingparametersreportedinTable5-1andcomparedwiththeexperimentaldata presentedinFigure5-3b...............................109 5-14Impedanceresponsefor0.3A/cm 2 generatedbyModels2and3for40 CusingparametersreportedinTable5-1:arealpartoftheimpedanceofthemodel responsecomparedwiththeexperimentaldatapresentedinFigure5-3b;and bimaginarypartoftheimpedanceofthemodelresponsecomparedwiththe experimentaldatapresentedinFigure5-3b....................110 5-15Fractionalsurface-coverageoftheintermediatesplottedaasafunctionofcell potential;andbasafunctionofcurrentdensity..................111 13

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6-1Full-scanXPSspectrumoftheusedsamplegeneratedatpassenergy89.45eV. XPSscansweretakenwiththePHI5100ESCAsystembyPerkin-ElmeravailableatMAICintheUniversityofFlorida.X-raysourcewasMganodewitha workfunction4.8eV.Thesamplewasscannedat300wattspowerinenergy rangeof1000-0eVbindingenergywithastepof0.5eVand30mSec/step...118 6-2Highresolutionperformedatpassenergyof22.36eVoftheXPSspectraon Ptpeaks.XPSscansweretakenwiththePHI5100ESCAsystembyPerkinElmeravailableatMAICintheUniversityofFlorida.X-raysourcewasMganodewithaworkfunction4.8eV.Thesamplewasscannedat300wattspower inenergyrangeof1000-0eVbindingenergywithastepof0.5eVand30mSec/step.119 6-3TEMimagesofcathodesurfaces.TEMstudywasperformedwithaJOELJSM2010FFieldEmissionElectronMicroscopeavailableatMAICintheUniversity ofFlorida.TheTEMmicrographsofcathodesurfacesweretakenat200kVacceleratingvoltageinbrighteldmode;afreshsample;andbusedsample...119 6-4TEMimagesofcross-section.TEMstudywasperformedwithaJOELJSM2010FFieldEmissionElectronMicroscopeavailableatMAICintheUniversity ofFlorida.TheTEMmicrographsweretakenat200kVacceleratingvoltagein brighteldmode;;afreshsample;andbusedsample...............120 6-5SEMmicrographsofcathodecross-sectionweretakenat15kVacceleratingvoltage.Thecross-sectionofthebothfreshandusedMEAwascutwithsharprazorandthesampleswerecoatedwithAu-Pd;afreshsample;andbusedsample............................................121 6-6Polarizationcurvegeneratedfromthesteady-statemeasurementfordierent timewith850CforH 2 asreactantattheanodeandairasoxidantatcathode. Theanodereactantstreamandcelltemperaturesweresetat40 0 Candthecathodereactantstreamtemperatureat35 0 C.Thefuelcellwasassembledwitha serpentineowchannel,andauniformporousGDL................122 6-7Impedanceresponsescollectedatat0.2A/ cm 2 asafunctionoftimesafunctionoftimewith850CforafunctionoftimeforH 2 asreactantattheanode andairasoxidantatcathode.Theanodeandthecelltemperaturesweresetat 40 Candthecathodetemperatureat35 C.Thefuelcellwasassembledwith aserpentineowchannel,andauniformporousGDL...............123 7-1Impedancedatarecordedwiththe850Cwithappliedcurrentdensityasaparameter.Theanode,cathode,andcelltemperaturesweresetto50 C......125 7-2Impedancedatarecordedwiththe850Cwithappliedcurrentdensityasaparameter.Theanode,cathode,andcelltemperaturesweresetto70 C......125 7-3Single-frequencyImpedancemeasurementsrecordedat0.1Hz,70 C,and1.4 A/cm 2 asfunctionsoftime:arealpart;andbimaginarypart..........126 14

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7-4Thestandarddeviationofthesingle-frequencyImpedancemeasurementsrecorded at1.4A/cm 2 and70 Casfunctionsoftime:aatafrequencyof100Hz;and batafrequencyof1HzaspresentedinFigure7-3.Thesolidlinerepresents theempiricalmodeldevelopedfortheerrorstructuregivenbyequation7{1..127 7-5Thestandarddeviationsfortherealpartoftheimpedanceasafunctionofcurrentdensitywithfrequencyasaparameterforcelloperationat70 C......127 7-6Standarddeviationsfortheimpedancedataobtainedatacurrentdensityof 0.4A/cm 2 .Thesolidlinerepresentstheempiricalmodeldevelopedfortheerrorstructuregivenbyequation7{1.Thedashedlinesrepresenttheasymptoticbehaviorofthemodelathighandlowfrequencies...............129 7-7Impedancemeasurementrecordedat0.4A/cm 2 and1Hzasfunctionsoftime at70 C:arealpart;andbimaginarypart....................130 7-8Thestandarddeviationofthesingle-frequencyImpedancemeasurementsrecorded at0.4A/cm 2 and70 Casfunctionsoftime:aatafrequencyof100Hz;and batafrequencyof1HzaspresentedinFigure7-7.Thesolidlinerepresents theempiricalmodeldevelopedfortheerrorstructuregivenbyequation7{1..131 7-9Standarddeviationsfortheimpedancedataobtainedatacurrentdensityof 0.4A/cm 2 :awithsystemtemperatureasaparameter;andbat70 Cwith anode/cathodeback-pressureasaparameter.Thesolidlinerepresentstheempiricalmodelfortheerrorstructuregivenbyequation7{1............132 7-10Standarddeviationsfortheimpedancedataobtainedatacurrentdensitiesof 0.4,1.0,and1.4A/cm 2 .Thesolidlinerepresentstheempiricalmodelforthe errorstructuregivenbyequation7{1........................132 7-11Normalizedstandarddeviationsfortherealpartoftheimpedancecalculated fromthedatashowninFigure7-3asafunctionofcurrentdensitywithfrequency asaparameter.....................................133 7-12TheimpedancedatarecordedusingtheMEAwithauniformGDL.Theanode, thecathode,andcelltemperaturesweresetat50 C................134 7-13NormalizedstandarddeviationsfortherealpartoftheimpedanceasafunctionofcurrentdensitywithfrequencyasaparameterfortheMEAwithauniformporedistribution.Theanode,thecathode,andcelltemperatureswereset at50 C.........................................135 7-14Standarddeviationsfortheimpedancedataobtainedatacurrentdensitiesof 0.02,0.1,and0.4A/cm 2 .Thesolidlinerepresentstheempiricalmodelforthe errorstructuregivenbyequation7{1.Theanode,thecathode,andcelltemperaturesweresetat70 C..............................135 15

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7-15Normalizedstandarddeviationsfortherealpartoftheimpedancemeasuredat 0.1HzforfuelcellscontainingtwodierentMEAsasafunctionofcurrentdensity.TheexperimentsfortheuniformMEAwereperformedat50 C,andthe experimentsforthenonuniformMEAwereperformedat70 C..........137 8-1Impedanceresponserecordedat70 Cwithcurrentdensityasaparameter.The fuelcellwasassembledwithanon-uniformGDLandaninterdigitatedowchannel............................................139 8-2RepresentationofthegraphicalanalysisofthedatapresentedinFigure8-1to obtaintheCPEexponent :athemagnitudeoftheimaginarypartoftheimpedance asafunctionoffrequencywithcurrentdensityasaparameter;andbCPEexponentobtainedfromtheslopeofpartaathighfrequencies...........140 8-3RepresentationofthegraphicalanalysisofthedatapresentedinFigure8-1to obtaintheCPEcoecient Q e andtheinterfacialcapacitance C e :aCPEcoecientobtainedfromequation8{1;andbtheinterfacialcapacitanceobtainedfromequation8{2..............................141 8-4CPEcoecient Q e asafunctionofcurrentdensitywithtimeasaparameter. TheimpedancedatawereobtainedundertheconditionsdescribedforFigure8-1.142 8-5Theinterfacialcapacitance C e ,obtainedfromequation8{2,asafunctionof currentdensitywithtimeasaparameter.Theimpedancedatawereobtained undertheconditionsdescribedforFigure8-1....................142 8-6ElectrochemicalparametersobtainedforthedatapresentedinFigures8-4and 8-5asafunctionofcurrentdensitywithtimeasaparameter:aCPEexponent ;andbOhmicresistance R e .........................143 8-7Impedanceresponserecordedatacurrentdensityof0.5A/cm 2 withsystem temperatureasaparameter.Theexperimentalsystemwasthesameasdescribed inFigure8-1......................................144 8-8Theinterfacialcapacitance C e ,obtainedfromequation8{2,asafunctionof systemtemperatureforthedatapresentedinFigure8-7..............144 8-9Theinterfacialcapacitance C e ,obtainedfromequation8{2,asafunctionof backpressureappliedforboththecathodeandtheanode.Theimpedancedata wererecordedat0.7A/cm 2 at70 C.Theexperimentalsystemwasthesame asdescribedinFigure8-1...............................145 8-10Interfacialcapacitanceasafunctionofcurrentdensityfordierentcombinationsofowchannelsandgas-diusionlayers.Theimpedancedatawererecorded at70 C.........................................146 8-11Interfacialcapacitanceasafunctionoftimewithoperatingandsystemconditionasaparameter.Theimpedancedatawererecordedat70 Cusingan MEAwithanon-uniformGDL............................147 16

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8-12CPEexponent Interfacial-capacitanceasafunctionoftimecorrespondingto theresultspresentedinFigure8-11..........................148 17

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LISTOFSYMBOLS b i TafelconstantinverselyrelatedtotheTafelslope,V )]TJ/F21 7.9701 Tf 6.587 0 Td [(1 c concentration,mole/cm 3 C 0 doublelayercapacitance, F/cm 2 D i diusivityofispeciesinionomeragglomeratesofthecatalystlayer,m 2 /s i currentdensity,mA/cm 2 K 3 rateconstant,mol/s K H 2 rateconstantofhydrogenoxidation,Acm/mol K H 2 O 2 rateconstantofperoxideformation,A/mol K O 2 rateconstantofoxygenreduction,Acm/mol K Pt rateconstantofPtoxidation,Acm/mol K Pt ; b backwardrateconstantofPtoxidation,A/cm 2 K Pt ; f forwardrateconstantofPtoxidation,A/mol K PtO rateconstantofPtOformation,Acm/mol n numberofelectronexchangedinthereaction R e membraneresistance,cm 2 t currentdensity,mA/cm 2 U cellpotential,V Z j imaginarypartofimpedance,cm 2 Z r realpartofimpedance,cm 2 diusionlayerlmthickness,m )]TJ0 g 0 G [-2249(maximumsurfaceconcentration,mole/cm 2 fractionalsurfaceconcentration,dimensionless i overpotential,V frequency,s )]TJ/F21 7.9701 Tf 6.586 0 Td [(1 18

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AbstractofDissertationPresentedtotheGraduateSchool oftheUniversityofFloridainPartialFulllmentofthe RequirementsfortheDegreeofDoctorofPhilosophy USEOFIMPEDANCESPECTROSCOPYTOINVESTIGATEFACTORSTHAT INFLUENCETHEPERFORMANCEANDDURABILITYOFPROTONEXCHANGE MEMBRANEPEMFUELCELLS By SunilK.Roy August2008 Chair:MarkE.Orazem Major:ChemicalEngineering Impedancespectroscopyprovidestheopportunityforin-situidenticationand quanticationofphysicalprocessesandhasbeenusedextensivelytostudythebehaviorof thefuelcell.However,akeyquestiontobeanswerediswhetherthefeaturesseeninthe impedanceresponsearecausedbyanartifactorrepresentaphysicalprocesstakingplace inthesystem.Themeasurementmodeldevelopedbyourgroupcanbeusedtoidentify thefrequencyrangesunaectedbybiaserrorsassociatedwithinstrumentartifactsand non-stationarybehavior. Impedancemeasurementswereperformedwiththe850Cfuel-cellteststationsupplied byScribnerAssociatesandwithaGamryInstrumentsFC350impedanceanalyzercoupled withaDynaloadelectronicload.Allelectrochemicalmeasurementswereperformed withatwo-electrodecellinwhichtheanodeservedasapseudo-referenceelectrode.The experimentswereconductedingalavanostaticmodeforafrequencyrangeof0.001-3000 Hzwith10mApeak-to-peaksinusoidalperturbation,andtenpointswerecollectedper frequencydecade.Ultrapurehydrogenwasusedastheanodefuel,andcompressedair wasusedasoxidant. Themeasurementmodelwasusedtoshowthatlow-frequencyinductiveloopswere, insomecases,fullyselfconsistent,and,therefore,theinductiveloopscouldbeattributed toprocessesoccurringinthefuelcell.Thenwedevelopedrst-principlemodelsthat 19

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incorporateprocessesthatmayberesponsiblefortheinductiveresponseseenatlow frequencies.Wefoundthatsidereactionsproducinghydrogenperoxideintermediatesand reactionscausingPtdeactivationcouldyieldinductiveloops.Thesesidereactionsandthe intermediatescandegradefuelcellcomponentssuchasmembranesandelectrodes,thereby reducingthelifetimethefuelcells.Thehypothesizedreactioninvolvingofperoxideand PtOformationweresupportedbymicrostructuralcharacterization. Amoresensitivemannerofusingimpedancespectroscopytogainaninsightinto theproblemofoodingwhichadverselyaectstheperformanceofthefuelcellwas established.Acomprehensivemodelforbase-levelnoiseinimpedancemeasurementsfor normalnon-oodedconditionswasdevelopedandactualnoiseinoodedconditionswas calculatedbytransientxed-frequencymeasurements.Acomparisonoftheactualnoiseto thebase-levelnoisewasusedtodetectonsetofooding. Also,graphicalmethodswereusedtointerpretimpedancespectraintermsof interfacialcapacitance.Theeectiveinterfacialcapacitancedecreasedwithincreasein currentanddecreasedslowlywithtime.Thedecreasesininterfacialcapacitancewith highercurrentdensitycanbeattributedtoanexcessamountofwateri.e.,ooding; whereas,thedecreaseininterfacialcapacitancewithtimemayberelatedtocatalyst dissolutionanddeactivation. 20

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CHAPTER1 INTRODUCTION PEMfuelcellsareelectrochemicalreactorsthatconvertchemicalenergyintoelectricalenergy.Thesearepromisingenergyconvertersinthe21 th centurybecauseoftheir pollutionfreecharacteristicandhighpowerdensity;however,severalissuesunresolved whichhavelimitedcommercializationofthisfascinatingtechnologyonalargescale. Costisonesuchfactor.Therequiredcatalyst,membraneandcellhardwaree.g.bipolar platesareexpensive,resultinginaveryhighinitialcost.Inaddition,hydrogengas,a fuelrequiredforfuelcells,isnotwidelyavailable,hasalowvolumetricenergydensity, thereforeisdiculttostore.Thisreducestheoperationalrangeofportablefuelcell devices.Storinghydrogenincarbonnanotubes 5 andmetalhydrides 6 hasreceivedagreat dealofattentionrecently.Inaddition,lessexploredmechanismssuchassidereactions andintermediatesperoxideformation, 7{9 platinumoxidationanddissolution, 10 carbon corrosion, 11 etc.reduceperformanceandlife-time.Watermanagementissues 12 suchas oodinganddryingalsolimitoperationofthefuelcellinnormaloperation,andunder start/stopcycling. Theobjectofthisworkwastoinvestigatefactorsandprocesseswhichadversely aectthefuelcelloperation.Thefactorsanalyzedinthisworkincludesidereactions andintermediatesinthereactionskinetics,andoodingofthefuelcell.Inthelastfew decades,muchattentionhavebeengiventoresearchanddevelopmentofthefuelcell; however,theroleofsidereactionsandreactionintermediatesiscomparativelyunexplored. Sidereactionsandtheassociatedintermediatescandegradethefuelcellcomponentssuch asmembranesandelectrodes,therebyreducingthelifetime,oneofthecrucialissuesinthe commercializationoffuelcells.Inaddition,impedancespectroscopyinconjunctionwith themeasurementmodelanalysiswasusedtogainaninsightintotheproblemofooding, anddryingwhichadverselyaecttheperformanceofthefuelcell. 21

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CHAPTER2 LITERATUREREVIEW Fuelcellsconvertchemicalenergyofareactiondirectlyintoelectricalenergywithout combustion.Fuelcellsgenerallyhaveminimummovingparts,whichmakethemhighly reliableandlong-lastingsystems.Theoretically,itcreateszeroenvironmentsandhealth hazardous.Thesefeaturesmakethefuelcellattractiveforalargevarietyofapplications, includingroadvehicles,decentralizedpowerproduction,residentialenergysystems,and evensmallerpotentialapplicationslikeportableelectronics. Fuelcellshavecomponentsandcharacteristicssimilartoanordinarybatterybut theydierinseveralrespects.Generally,batteriesceasetoproduceelectricalenergywhen thelimitingchemicalreactantsareconsumedwhereasfuelcellsproduceelectricalenergy foraslongasreactantsaresupplied.Batteriesscalepoorlyatlargesizeswhilefuelcells scalewellfromthe1WrangecellphonetotheMWrangepowerplant.Fuelcellsoer potentiallyhigherenergydensities,andcanbeinstantlyrechargedbyrefueling,while batteriesmustbethrownawayorpluggedinforatime-consumingrecharge.Materials usedinbatterieselectrodeshavetogothroughchangesduringcharing/discharging cycles,whicheventuallyresult,intodegradedenergyoutputand/orcatastrophicfailure. 13 TheperformanceoffuelcellsisnotsubjecttoCarnoteciencyunlikeheatengines. Fuelcellsareoftenfarmoreecientthancombustionengines.Combustionalsohas disadvantagesofundesiredgasessuchCO,CO 2 ,NO x ,SO x ,andparticulateemissions. Althoughtherearedierenttypesoffuelcells,PEMfuelcellsareregardedasthe mostsuitablefuelcellatmoderatetemperature-100 Cduetotheirhighpower density,compactdesign,minimumpollutantsemissions.Fuelcellshavebeenknownfor alongtime.In1839,WilliamGrove,wascreditedwithrstdevelopingtheprincipleof thefuelcell.Groveutilizedfourlargecells,eachcontaininghydrogenandoxygen,to produceelectricalpowerand,waterasabyproduct. 14 TheschematicofaPEMFCis showninFigure2-1a.ThefuelcellusesaPEMasanelectrolyte.Hydrogengasasfuel issuppliedattheanodeandoxygengasorairasoxidantissuppliedatthecathode.The 22

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followingtwohalf-cellreactions2{1and2{2takeplaceattheanodeandthecathode respectively,andequation2{3istheoverallreactioninthefuelcell. H 2 2H + +2e )]TJ/F15 11.9552 Tf 170.857 -4.936 Td [({1 O 2 +4H + +4e )]TJ/F19 11.9552 Tf 10.406 -4.936 Td [(! 2H 2 O{2 O 2 +2H 2 2H 2 O{3 ThemaincomponentsofthefuelcellareshowninFigure2-1b.Thefuelcelltypically consistsofamembrane,twoelectrodes,gasdiusionlayersGDL,andbipolarplates. 2.1ElectrochemistryandLossesintheFuelCell ThechangeinGibbsfreeenergy G ismeasureofthemaximumworkobtainable fromthereaction. G fortheoverallreaction2{3inthefuelcellis-237.14kJ/moleat standardconditions.Cellpotentialcanbecalculatedbyequation2{4. G = nFE 0 {4 whereFisFaradayconstantequalsto96485C/mole,nisnumberofmolesofelectrons involvedinthereaction,and E 0 iselectrodepotential.Equationgivesvalueofcell potentialas1.23VwhichisreferredasanopencircuitvoltageOCV. G isafunction ofoperatingconditionssuchasoperatingtemperatureandpressure,hencetheOCV alsodependsontheoperatingconditionsofthecell.Thedependencyofthepotentialis describedbytheNernstequationwhichgivesthethermodynamicvoltageoffuelcells. E nernst = E 0 + RT nF ln P H 2 P O 2 {5 where R isUniversalgasconstant, T istemperature, P i ispressurefor i reactants.The actualvoltageoutputofafuelcellislessthanthethermodynamicallypredictedNernst Equationvoltageduetoseveralirreversiblelosses. 2 Aplotofcellvoltageversuscurrent densityknownaspolarizationcurveFigure2-2,whichshowsvariouslossestaking placeinthefuelcell.Theactualvoltagedrawnfromthefuelcellshouldbeequaltothe 23

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a b Figure2-1:Illustrationofthefuelcelltakenfromliterature 1 ;aowdiagram;andb components. 24

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Figure2-2:ApolarizationcurveforafuelcelltakenfromLin etal. 2 ,showingthelosses associatedwithreactionkinetics,internalelectricalresistance,andmasstransports. dierenceoftheoreticalvoltageandthevariouslosses: E actual = E nernst )]TJ/F22 11.9552 Tf 11.956 0 Td [( act: )]TJ/F22 11.9552 Tf 11.955 0 Td [( conc: )]TJ/F22 11.9552 Tf 11.955 0 Td [(IR e )]TJ/F22 11.9552 Tf 11.955 0 Td [( parasite {6 where E actual isactualvoltage, E nernst isthermodynamicallypredictedvoltage, conc: is concentrationloss, act: isactivationloss, parasite isparasitelossand IR e isOhmicloss. 2.1.1ActivationLoss Atlowcurrentdensity,thecellvoltagedropsrapidlyduetosluggishnessofelectrokineticsatelectrodes.ORRisslowerandcanaccountformostoftheactivationlosses. Inaddition,competingreactionsoccurattheoxygenelectrodesuchasoxidationof theplatinum,corrosionofcarbonsupport,andoxidationoforganicimpuritiesonthe electrodecanleadtolossofvoltage.TheactivationlosscanbederivedfromtheButlerVolmerequationas: act: = RT F ln i i 0 {7 25

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where i iscurrentdensity, i 0 isexchangecurrentdensity,and isapparenttransfer coecient. Activationlossesareminimizedbymaximizingtheexchangecurrentdensity.The exchangecurrentdensityisafunctionofthecatalystmaterialandtheelectrochemical activesurfacearea.Theelectrodesaremadehighlyporousbydispersing,nano-scale particlesofplatinumonelectronicconductorporouscarbonsupportmixedwithanion conductiveelectrolytetoenhancetheoverallactivearea. 2.1.2OhmicPotentialLoss Ohmiclossesariseduetotheresistanceofthematerialselectrodes,membraneto owofspeciessuchasprotontransportthroughthemembraneandelectrodes,electron transportthroughelectrodes,bipolarplates,andcollectorplates.Itappearsasalinear partinthemiddleofpolarizationcurve.Themagnitudesofthesepotentiallossesdepend onthematerialsusedintheconstructionofthefuelcellandtheoperatingconditionsof thecell.Mostoftheohmiclossarisesfromtheionicresistanceintheelectrolyte.The thinnerthemembrane,thelowerthisloss.Thinnermembranesarealsoadvantageous becausetheykeeptheanodeelectrodewetbyback-diusionofwaterfromthecathode, howeververythinmembranecouldleadtopinholeformationandthereforegascrossover. Itisalsoreportedthattheinterfacialresistancebetweenthegasdiusionlayerand thebipolarplatemightcontributesignicantlytothetotalohmicresistance,especially whenalternativebipolarplatematerialssuchassteelareused. 15 2.1.3ConcentrationOverpotentialLoss Athighcurrentdensities,thevoltageoutputofthefuelcellonceagaindropsrapidly duetomass-transportlimitationsattheelectrodes.Theconcentrationlossescanbe evaluatedas: conc: = RT F ln i lim i lim )]TJ/F22 11.9552 Tf 11.955 0 Td [(i {8 where i lim islimitingcurrentdensities. 26

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Thislossmainlyarisesfromthemass-transportresistanceincatalystanddiusion layers.However,mass-transportinthediusionlayercanalsobeaectedbythechannel geometryoftheoweldplate.Inaddition,athighcurrentdensityheftyamounts ofwaterareproduced,whichcausesoodingofthecathodesurfaceandinhibitsthe transportofreactantsaswellasionicspecies. Thephysicalpropertiesofthediusionlayerssuchasporositycanbeaectedby severalfactors,whichmayresultintomass-transportoverpotential.Athighcurrent densities,theporosityisreducedcomparedtothedrystatebythepresenceofliquid water.Theporosityofthediusionlayersisalsoaectedbythecompressionforceapplied whileassemblingthefuelcell.Excessivecompressionreducestheporositywhichhinders gas-transport,whereastoolittlecompressionmaycauseanincreaseincontactresistances. Themass-transportlossatveryhighcurrentdensitiesisalsoattributedtodryingofthe anode. 16 2.1.4ParasiticPotentialLoss Eveninthelimitofzerocurrentinthefuelcell,theoutputvoltageofthecellisless thanthethermodynamicallypredictedvoltage.Thisdecreaseisduetogascrossoverand undesiredelectronleaksacrosstheelectrolytemembrane.Fuelcrossoveristheamount offuelthatcrossesthemembranefromtheanodetothecathodewithoutbeingoxidized attheanodecatalystlayer,whichresultsinalossoffuel.Internalcurrentistheowof electronfromtheanodetothecathodethroughthemembraneinsteadofgoingthrough theexternalcircuit.Manyotherunknownprocessescanalsocontributetothisloss;oneof theprocessescanbeprotontransportthoroughthemembranewhichdenedasconvection overpotentialgivenas: 17,18 conv: = FC H + l m k {9 where C H + isprotonconcentration, iswatervelocityinthemembrane, l m isthicknessof membrane,and k ismembraneconductivity. 27

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Figure2-3:ChemicalstructureofNaontakenfromWeberandNewman etal. 3 2.2PEMFuelCellComponents 2.2.1Membrane Athinelectrolytelayerspatiallyseparatesthehydrogenandoxygenelectrodesand ensuresthatthetwoindividualhalfreactionsoccurinisolationfromoneanother.Itmust notallowelectronstocross,butmustallowprotonstopasseasily.Themembraneshould possesseshighionicconductivity,highstabilitywatermanagement,lowfuelcrossover, highmechanicalstrength,goodelectronicinsulation,goodseparationofreactants,high chemicalandthermalstability,andlowcost. 19 Thestandardmembraneismadeofsulfonatedpoly-tetra-ouroethylenePTFEas backbonewheresomeoftheuorineatomsarepartiallysubstitutedbychainscontaining sulfonicacid.ThismembranematerialproducedbyDuPontcarriesthebrandnameas Naon.MolecularformulaofNaonisshowninFigure2-3.Thebackbonehydrophobic phaseprovidesNaonwithanexcellentoxidativestability,mechanicalintegrity,and limitstheswellingofmembranewhilesulphonicgrouphydrophilicphasehelpsproton transport.Thehighelectronegativityoftheuorineatomsbondedtothesamecarbon atomasthesulfonicacidgroupmakesthe )]TJ/F15 11.9552 Tf 9.298 0 Td [(SO 3 Hasuperacid. TheexactstructureofNaonisnotknownhowever,itisreportedthatelectrostatic interactionsbetweentheionsandtheion-pairscausetheionicgroupstoaggregate andformtightlypackedregionsreferredasclusters.Theseinteractionsenhancethe intermolecularforcesandconsiderablyinuencethepropertiesoftheparentpolymer. 28

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SmallangleX-rayscatteringandneutronscatteringexperimentscanbeusedtoindicate ionicclusteringinNaon. TheprotonconductivityofNaonisdependantonitshydrationstate.Inthedry state,Naonisapoorionconductor,butionicconductivityincreasessharplywith watercontent. 3 Indrystate,protonsmaymigratefromoneacidgrouptoanotherinthe network;theassociatedactivationenergyisrelativelyhigh,resultinginrelativelylowionic conductivity.However,whenwaterllstheporenetwork,theprotonsaresolvatedby oneormorewatermolecules.Watersolvationpartiallyscreenstheprotoncharge,thus loweringtheactivationenergyformigration.Toensuremembranehydrationhumidied gasesaregenerallyfedintothefuelcell. Naondehydratesattemperatureabove80 C;thedehydrationcancausemembrane toshrink,reducingcontactbetweenelectrodesandmembranethereforehighercontact resistance.Theshrinkmayalsocausepinholesformation,leadingtoreactantcrossover. 20 Naonalsoshowsconsiderabledeteriorationintheconductivityandthemechanical strengthabovetheglasstransitiontemperatureca.110 C. Alifetimeofover60,000hoursunderfuelcellconditionshasbeenachievedwith commercialNaonmembranes.However,evenextremelystableNaoncansuerfrom degradation.UsingXPSanalysisoftheMEAbeforeandafterfuelcelloperationHuang etal. 21 hasfoundthat )]TJ/F15 11.9552 Tf 9.299 0 Td [(CF 2 )]TJ/F15 11.9552 Tf 13.2 0 Td [(groupsofNaonaredestroyedunderelectrochemical stress,yieldingthe )]TJ/F15 11.9552 Tf 9.298 0 Td [(HCF )]TJ/F15 11.9552 Tf 13.201 0 Td [(or )]TJ/F15 11.9552 Tf 9.299 0 Td [(CCF )]TJ/F15 11.9552 Tf 13.2 0 Td [(congurations.Undertheanodepotential,the hydrophobicparte.g.,uorocarbonmayreactwithcarbonorhydrogenatoms,resulting nallyinthedegradationoftheelectrolyte.Also,thiskindofhydrocarbonmembranes arepronetooxidativedegradationbyperoxideintermediates.Thehighcostandhigh methanolpermeabilityoftheuorinatedpolymersalsourgethenecessitytodevelop alternativeproton-conductingpolymers. 29

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Agreatnumberofpolymermaterialshavebeenpreparedandfunctionalisedfor possibleelectrolytesforfuelcells.Improvementsinthemembranestructureandconductivitywereachievedbyproducingcompositemembranes.Usually,PTFEisaddedinto Naontoimprovemechanicalstrength,thereforemuchthinnerlayerofPTFEblended NaoncanbeusedwhichhasadvantageoflowOhmicdropascomparedtopureNaon. However,thinnerPTFEdopedNaonhaslargerpermeationratethuslowOCV. 22 The largerpermeationresultsinhighercrossoverofreactants,andheatgeneratedbyreaction duetolocalhotspotscreatelocalizedmembranedrying,andhighermembraneresistance. Thecrossoverofreactantshavebeenutilizedtomakethesemembraneself-humidifyingby providinghighlydispersedPtparticlesinthemembranewhichenableslocalizedformation ofwaterthoughuniformdistributionofPtisnotachieved.Toexploitthisidea,verythin layersofPt/Chavebeenusedbothsideofthemembranewhichreducesthecrossoveras wellasensureformationofwatertohumidifymembrane. 22 Also,acompoundCs 2 : 5 H 0 : 5 PW 12 O 40 hasbeeninvestigatedtoincorporateinto Naon/PTFEcomposite,betterperformanceobservedisattributedtostrongacidic andhydrophilicnatureofthecompoundwhichenhancewaterretentioncapacity. 23 A compositemembranebyblendingNaonwithpolyvinylideneuorideisinvestigated thoughtheobservedprotonconductiveismuchlowerthanNaonwhichisdueextreme hydrophobicityofuoridecomponents.Toimprovewateranityandprotonconductivity, thecompositeischemicallymodiedbydehydrouorinationandtreatmentwith H 2 SO 4 24 W.L.GoreandAsahiChemicalshavesuccessfullyreinforcedperuorosulfonicacid membraneswithTeonfabric. 25 Carbonnanotubeshavebeenproposedtoincorporate intoNaontoincreasemechanicalstabilityduetotheirexceptionalenforcingbre strength,lowdensityandhighaspectratio,however,sincecarboniselectronicconductor whichcanleadtoelectronicshort-circuitthusreducingtheOCV. 26 Byoperatingfuelcellsathighertemperature,theoxygenreductionkineticsand carbonmonoxidepoisoningproblemsareimproved.Compositesaremadebyswelling 30

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theperuorinatedionomericmembranewithanionicliquidtoimproveitshightemperaturestability. 27 ToimprovethehydrationcharacteristicsofNaon,nanoparticlesof hygroscopicmetaloxidessuchasSiliconoxideisincorporatedintoNaon.Thewater retentioncapacityisimproveswhichenableuseofthiscompositeatelevatedtemperature however,thecompositeshowshigherohmicresistancemaybeduetodisruptionofproton conductionpathinNaonbypresenceofsiliconoxideparticles. 20 Non-Naonmembraneswerealsoinvestigatedforintermediate-temperatureoperationoffuelcells. 28,29 Usually,phosphatebasedprotonconductorsareblendedwith inorganiccompoundsuchassilicateormetalwhichprovidemechanicalstabilitytothe composite.SincePO )]TJ/F21 7.9701 Tf 6.587 0 Td [(3 4 isthermallystableabove200 CwhileprotonsourcesSO )]TJ/F21 7.9701 Tf 6.586 0 Td [(2 4 inNaondecomposesabove200 C.Severalcompositemembranesforhightemperatureapplications 30{37 areinvestigated.Compositemembranewereexploredbydoping Naonwithdierentheteropolyacidssuchasphosphotungsticacid,silicotungsticacid, phosphomolybdicacid,andsilicomolybdicacid. 32 Heteropolyacidstypicallyexistinthe hydratedphasewith30to6watermoleculesperacidmolecule;therationalebehindusing theseacidsistoutilizetheadditionalwatermoleculeforhumidicationofmembrane especiallyathighertemperature.Verylittleimprovementintheperformanceisrecorded whichisattributedtolargerparticlesoftheseadditiveswhichareunabletohelpconductionofprotonsthroughthemembranecluster.Itisalsoreportedthattheseacids dissolve;Molybdateatomsareobservedoncatalystlayerwhichmaybeduetomigration ofmoleculestocatalystlayerthoughadditiveswithTungstenisrelativelystableinthe membrane.Toimproveabovedisadvantages,theseacidsarestabilizedbycationswhich ensureuniformdispersionofsmalleracidparticlesandthereforehelpcreateeective bridgingbetweenionicdomains. 32 Heterocyclicaromaticpolymerareusedduetotheirexcellentthermalandchemical resistanceandsuperiormechanicalintegrity.Someofthemostpromisingcandidatesfor proton-exchangemembranesarehighperformancepolymers,ie.polyimides,polyether 31

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ketones,polyaryleneethersulfones,polybenzimidazoles,etc.Advantagesofusingthese materialsarelowercostthanperuorinatedmembranes,inclusionofpolargroupsto improvewateruptakeoverarangeoftemperatures,andthepossibilityofrecyclingby conventionalmethods. Thesix-memberedringofthenaphthalenicpolyimideismuchmorestabletohydrolysis,thismembraneisbettersuitedforfuelcellapplications 38 whileve-memberedring polyimideswhichmayundergohydrolysisofthephthalimidestructureunderstrongacid conditionsquicklyleadstochainscissionandcausesthemembranetobecomebrittle. 39 Thisindicatesthatthestabilityofthehighlycross-linkedmembranesisnotonlycaused bycross-linkingofthepolystyrenechains,whichslowsdownthelossof )]TJ/F15 11.9552 Tf 9.299 0 Td [(SO 3 H fromthe membranes,butalsobyreducedgascrossoverand,therefore,reducedHO 2 andOH )]TJ/F15 11.9552 Tf 10.987 -5.014 Td [(formation.Highdegreesofcross-linkingmorethan12couldimprovethestability,however, thesimultaneousincreaseofmembraneresistancemightnotbetolerable.Theoptimum membranethickness,which,asacompromisebetweengascrossoverandresistance,must befound.AnothercrucialpointistheC )]TJ/F15 11.9552 Tf 11.955 0 Td [(O )]TJ/F15 11.9552 Tf 11.955 0 Td [(Cbondbreaking,initiatedbyattackof OH )]TJ/F15 11.9552 Tf 7.085 -5.015 Td [(.InthepresenceofbothOH )]TJ/F15 11.9552 Tf 10.987 -5.015 Td [(radicalsandoxygen,completedegradationofthe aromaticringscanbeachievedwithinafewhours.Inviewofthis,thesaturatedand peruorinatedNaonwhichismuchmoreinerthasaninherentadvantageoverthenew membranesbasedonaromatichydrocarbons. 2.2.2Electrodes Themajorrequirementsforaneectivecatalystarehighactivity,highelectricalconductivity,highprotonconductivity,lowcorrosion,highporosity,highmechanicalstrength, andhighlyporoustoensuregoodgasaccess.State-of-the-artcatalystsutilizenano-sized platinumparticles-10nmsupportedonahighsurfaceareacarbonpowder-50 nm.Whileplatinumprovidesthecatalyticactivity,thecarbonprovidestheelectrical conductivitynecessarytoharvestelectronsto/fromtheactivesites.Thecarbon-supported platinumPt/Cstructureoersahighcatalyticsurfacearea,signicantlyreducingthe 32

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Figure2-4:AschematicrepresentationofmembraneelectrodeassemblyMEAtakenfrom literature 1 requiredplatinumloadinggenerallylessthan0.5mgPt/cm 2 .ThePt/Cpowderismixed withsmallquantityoftheNaonelectrolytetoensureprotonconduction.Inpractice, thethicknessofthecatalystlayerisbetween10-50micron.Whileathinlayerispreferred forbetterreactantsdiusionandcatalystutilization,athicklayerincorporateshigher catalystloadingthuscatalystlayeroptimizationrequiresadelicatebalancebetween masstransportandcatalyticactivityconcerns.TodistributePtonCarbonuniformly,a surfactantissuggestedwhichstabilizesthenanoparticlesofPtandpreventaggregation. 40 Also,useofanoptimumamountofammoniumcarbonateasanadditivetocatalystlayer issuggestedwhichaidsinporeformingthusimprovesthemass-transportlimitations. 41 Toreducethecostofcathodecatalyst,alloyssuchasPlatinum-IridiumPt )]TJ/F15 11.9552 Tf 11.955 0 Td [(Ir, 42 Pt-CobaltPt )]TJ/F15 11.9552 Tf 11.955 0 Td [(Co, 43 Pt-IronPhosphatePt )]TJ/F15 11.9552 Tf 11.955 0 Td [(FePO 4 44 havebeeninvestigatedas possiblecathodematerials.Theproblemwiththesetransitionmetalalloysaredurability, theseareunstableinacidicenvironmentofthefuelcell.AdditionofNiinPt-alloy Pt 3 Ni 1 ,wasobservedtoshortenthePt-Ptinteratomicdistance,thusresultingin strongerbondingreducingdissolutionandlossofcatalyst.However,thealloyshows higherinterfacialresistance,anddissolutionofmetalinfuelcellenvironment,and subsequentdiusionofNiintomembranecandegradethelifetimeoffuelcell. 45 Similarly, lessexpensivecatalystsbyalloyingPtwithFe )]TJ/F15 11.9552 Tf 11.955 0 Td [(Ni )]TJ/F15 11.9552 Tf 11.955 0 Td [(Cowereexplored;theinitial 33

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activitiesforPt )]TJ/F15 11.9552 Tf 11.955 0 Td [(Fewasfoundtobethehighest;however,dissolutionandsubsequent leachingofmetalintothemembranewerefoundtocauseadditionaldeteriorationofMEA andthereforereducethelifetime. 46,47 Non-platinummaterialssuchasZirconiumoxide 48 andTantalumoxynitride 49 isalso investigatedforcathodecatalyst.Solderived 50 materialswithtransitionmetalsuchas CobaltCooncarbonsupportwhenaddedwitharomaticligand1,2-phenylenediamine canalsobeusedasacathodecatalyst.TungstenCarbideWCwithadditionofTantalumTaisalsoinvestigatedforacatalyst;theTantalumisaddedtoenhancethe corrosionresistanceofthecarbide.ItisreportedthatTantalumformsanalloyW )]TJ/F15 11.9552 Tf 11.955 0 Td [(Ta withTungstenwhichenhanceselectroactivityandcorrosionresistanceofthematerial. 51 A single-walledcarbon-nanotube-basedprotonexchangemembraneassembliesforhydrogen fuelcellswasalsoexplored. 52 Theidealcarbonsupportshouldpossesshighchemical/electrochemicalstability,good electronicconductivity,andasuitablyhighsurfaceareaandporesizedistribution. 53 A carbonblackcommerciallyknownasVulcanXC72CabotCorp.isthemostcommon usedcatalystsupport.However,ithasrandomstructureandbroadpore-sizedistribution whichleadtoevendistributionofNaon.Also,themicro-porecannotbelledbyNaon becauseNaonparticlesareusuallybiggerthantheporesize,thereforePtparticles insidethemicro-porearenotaccessibletoelectrochemicalreactionthusreducescatalyst utilization. 54 BetterperformanceisobservedusingorientedCarbonnanotubesCNTs insteadoftheconventionalcarbonascatalystsupport.Electronicconductivityand gaspermeabilityareexpectedtobemuchhigheralongtheCNTsthanacrossthetube, andalsoorientedCNTsmayexhibitsuperhydrophobicity,whichcanfacilitatewater removalwithintheelectrode;thesefactorsmaybeattributedtotheimprovementin theperformance. 55 ItisalsoreportedthatPt/CNTshasbetterlifetimecomparedto Pt/C. 56 However,carbonnanotubesconsistofhollowcylinder,sohigherdispersionofPt particlesaredicultinsidethenanotubesbecauseofdiameter-to-lengthratioinasingle 34

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nanotubes.Toovercomethisproblem,catalystsupportbasedoncarbonaerogel-basedwas exploredandbetterperformancewasobserved. 54 GoldhasbeenalsoinvestigatedasapossiblecatalystsupportwhichshowscomparableelectrochemicalactiveareaandsotheperformancewithCarbononmuchlowerPt loadingsthoughthecostofGoldisaconcern. 57 Aconductingpolymercomposite 58 for catalystsupportmaterial,wastested.Thecompositeconsistsofanelectronicconductive ende.g.polyprrole,poly,4-ethylenedioxythiophene,andaprotonconductingende.g. polystyrenesulfonate.Ithasexcellentperformanceforoxygenreductionreactionhowever; adecimalperformanceisobservedforhydrogenoxidationbecauseatanodepotentialthe electronicconductingfunctionalgroupbecomesinactive.TungstenOxideWO 3 wasalso proposedasapossiblecatalystsupportasitisastableoxideandnotproneto PtO formationcomparedtoconventionalcatalystsupport. 59 Itisalsomorethermallystablethan Carbonwhichenablesitsuseinhightemperatureoperationofthefuelcell.Polyaniline dopedtriuoromethanesulfonicacidisinvestigatedasaprotonconductingmaterialtobe usedincatalystinsteadNaon.Itsbrousnaturehelpsdistributeparticlesuniformly,and ensuresbetterconnectionofreactionsites,andthusenhancesPtutilizationcomparedto Naon. OptimizationofcatalystcompositionwithrespecttoPt,andNaonloadingshas beeninvestigatedthoroughly.AnoptimalcompositionofNaonhasobserved;tolittle Naonwasinsucientforprotonconductionthusincreasesionicresistance,ontheother hand,toomuchNaon,maycoverPtparticlesformingalmsthathinderselectron transporttoPtthereforereducescatalystutilization.Also,itllscarbonporeshindering gastransportandwaterremoval.SinceNaonisnotmechanicallystableathigherwater contentsoincaseofoodingtoomuchNaoncanleadtobreak-downofcatalystlayer. NaonloadingusuallyresultsinOhmicandmass-transportdiusionlimitationinthe fuelcelloperation. 35

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AnoptimallmthicknessforgivenNaonnloadingwassuggested. 60 ANaon loadingof1.3mg/cm 2 wasfoundtocorrespondtotheoptimallmthicknesssucient totransportprotonwithouthinderingelectronandgastransport.Naonloadinggreater thantheoptimalvalueresultsinanadditionalarcatlowfrequencyinimpedanceresponse representinggas-diusionlimitation. 61 FurtherimprovementinNaonloadingisobtained to0.8mg/cm 2 byusingacatalystsupportbetweencatalystlayerandgasdiusionlayer inthefuelcell. 61 ElectrodesconsistingoftwolayerswithdierentNaonloadingwasalso proposed,butnobetterperformancewasobtained. 62 2.2.3GasDiusionLayers Thefunctionsofthegasdiusionlayersaretoprovidestructuralsupportforthe catalystlayers,passagesforreactantgasestoreachthecatalystlayersandtransportof watertoorfromthecatalystlayers,electrontransportfromthecatalystlayertothe bipolarplateintheanodesideandfromthebipolarplatetothecatalystlayerinthe cathodeside,andheatremovalfromthecatalystlayers.Thecommonmaterialsforthe GDLarecarbonpaperandcarbonclothwhichincorporatesahydrophobicmaterial, suchasPTFEtopreventwaterfrompoolingwithintheporeofthebackinglayer. Furthermore,PTFEcreatesanon-wettingsurfacewithinthepassagesofthebacking materialwhichfacilitatesproductwaterremovalonthecathode. Thephysicalpropertiessuchasporesizeandstructure,hydrophobicity,andthickness ofGDLplaymajorroleinmass-transportprocesses.Kong etal. 63 reportthatmacroporespreventoodingandthusimprovesperformance.Tomodifyporestructure,poreformingagentssuchasLi 2 CO 3 wereinvestigated.Someauthors 64{66 suggestedusing atwo-layerstructureasagasbacking.Thelayerclosertotheelectrodeisknowas thediusionlayersandshouldhaveanerstructuretoensurethatasmanycatalyst particlesaspossibleareinelectriccontact.Capillaryactionassociatedwiththener porestructureenhancetransportofreactantstothecatalystsites.Thediusionlayer distributesreactantsmoreuniformly,enhancesmechanicalcompatiblywithcatalystlayer, 36

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andreducescontactresistance. 67 Thelayerfacingtheoweldplateisknownasthe backinglayer.Itshouldbethickerandshouldhaveacoarserstructure. Applicationofanoptimumcompressionforcewhileassemblingthefuelcellhasbeen advocated. 66 ThecompressiveforceshouldbeestimatedbasedonGDLthicknessand gasketcompression:toomuchcompressiveforcemightreducetheporositychanging waterholdupandthusreducingelectrochemicalactiveareaandcreatingmass-transport problems,whereastoolittleforcemightincreasecontactresistances.Itwasalsoreported thatthecompressionparticularyreducesporosityandthicknessofGDLunderland portionofchannelwhichspeciallyinuenceshighercurrentdensitybylimitingtransport ofoxygen. 18 SinteredTitaniumwasalsosuggestedtobeasaGDLmaterialduetoits lowercost,thoughithashighcontactresistancewithMEA.Theresistancecanbereduced byapplyingPtcoatingontheGDLsurface. 68 2.2.4BipolarPlates AplateincontactwiththeGDLisknownasbipolarplate.Theplateusually incorporatesowchannelforreactantsfeedandmaycontainconduitsforheattransfer. Thedesiredcharacteristicsofbipolarplatematerialsarehighelectricalconductivity, impermeabilitytogases,highthermalconductivity,lightweight,highcorrosionresistant, andeasytomanufacture. Thecommonmaterialsusedforbipolarplatesaregraphite,andmetalssuchas stainlesssteel,aluminum,orcompositematerial.Graphiteplatesmeetmostofthe requirementsforoptimalfuelcellperformancebuttheow-channelmachiningofgraphite issoexpensivethatgraphiteplatescantakeuptohalfthecostofafuelcellsystem. Metallicplatesarecheapandeasytomanufacture,however,thesehaveahighcontact resistanceduetotheformationofmetaloxidelayerbetweentheplateandtheGDL. Pozio etal. 69 hasreportedthatIron,acontaminationinstainlesssteelSS316Lbipolar plates,reactswithelectrolyteNaonanddegradesit.Aferritestainlesssteelsample withdierentcompositionofChromiumhasbeenreportedasbipolarplate,ithasfound 37

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thatthesamplewithhighestchromiumcontentwasbettermaterialforbipolarplate. Compositescanoerthecombinedadvantagesofhighelectricalandthermalconductivity ofgraphiteplates,andlowmanufacturingcostofmetallicplate. 70 Middleman etal. 71 has reportedgraphitelledpolymercompositeforpossiblebipolarplatematerialdeveloped byNedstackArnhem,TheNetherlands.Oh etal. 72 havestudiedelectricalandphysical propertiesofpolymercompositematerialwithPd-Nicoatingforbipolarplate.These materialshavelowerelectricalinterfacialresistanceandhighersurfaceroughnesswhen comparedwithconventionalresin-impregnatedgraphitematerial. Thefunctionsofthebipolarplatearetoprovidethepathwaysforreactantgas transport,andelectronconductionpathsfromonecelltoanotherinthefuelcellstack, separatetheindividualcellsinthestack,carrywaterawayfromthecells,andprovide coolingpassages.Platematerialandtopologiesfacilitatethesefunctions.Common topologiesusedarestraight,serpentine,orinter-digitatedowelds.Serpentineisthe mostcommongeometryfoundinfuelcellprototypes.Theadvantageoftheserpentine patternliesinthewaterremovalcapability.Onlyoneowpathexistsinthepattern, soliquidwaterisforcedtoexitthechannel.However,inlargeareacells,aserpentine designleadstoalargepressuredrop.Severalvariationsoftheserpentinedesignhave beeninvestigated,suchastheparallel-serpentineconguration.Theinterdigitateddesign promotesforcedconvectionofthereactantgassesthroughthegasdiusionlayer.Subject tomuchrecentattention,researchhasshownthatthisdesignprovidesfarbetterwater management,leadingtoimprovedmasstransport. 73 Buttheforcedconvectionthrough thegasdiusionlayerleadstosignicantpressuredroplosses.However,thereisevidence thatthismajordisadvantagemightbepartiallyovercomebyemployingextremelysmall ribspacing. 74 38

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2.3DegradationMechanismsinFuelCells Thedurabilityisoneofthemostcriticalissuesincommercializationoffuelcells. 75 Thedegradationandperformancelosscanbeaectedbyseveralfactors,someofthemare discussinfollowingsections. 2.3.1HydrogenPeroxideFormation Hydrogenperoxide,astrongoxidizingagent,degradesmaterialsthuslimitsthe performanceandlifetimeofthefuelcell.Theperoxidecanbeformedbytwo-electron reductionofoxygeninthefuelcellenvironmentasfollowingsuggestedbyresearchers. 7,8,76 O 2 +2H + +2e )]TJ/F19 11.9552 Tf 10.405 -4.937 Td [(! H 2 O 2 {10 Evidenceoftheperoxideformationhasinvestigatedrigorously.Arotating-ring-diskelectrodestudy 77 revealedthatformationoftheperoxideonplatinumparticlessupported oncarboncatalystusedinthefuelcellisquitepossiblebytwo-electronreductionwhile theformationwasnotobservedoncleanbulkplatinum.Theperoxideformationwas reportedtobemorepronouncedonPt/CascomparedwithpurePtsurfaceandthe formationisgreatlyenhancedbyadecreaseintheagglomerationofPtparticles. 77 An experimentalarrangementwasillustratedtodetectin-situhydrogenperoxideformation inthefuelcell. 78 Therecordedin-situCVhavetwopeaksonecorrespondingtoperoxide formationandotherPtOformation.Theyalsofoundthatthinnermembranehashigher peroxideconcentrationwhichispossiblebyOxygencrossoverfromthecathodetothe anode. 78 Inprocessing,themembraneNaonisusuallypre-treatedinboilingperoxide whichcanalsobeasourceforperoxideinmembranetotriggerformationoftheseradicals leadingtodegradation. 79 Theperoxideformationhasbeenalsoreportedincaseofair bleed.IncaseofCOcontaminationinfuel,air-bleedisdonetopromoteoxidationofCO toCO 2 cleansingbutonlyasmallfractionoffedoxygenisusedfortheoxidation,while majorfractionofoxygencompeteswithORRandproduceshydrogenperoxide. 80 39

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Theformationofperoxideatcathodehasbeenreportedduetocrossoverofhydrogen fromanodetocathode.Theeectoftemperatureandhumidityonperoxideformation kineticswasstudiedshowinghigherconcentrationofperoxideatthecathodecompared toattheanode. 81 Theperoxideformationinsidethemembranewasalsoobserveddueto presenceofplatinumband. 82 TheformationofPtbandispossibleduetodissolutionand migrationofPtparticlesfromelectrodesandredepositioninsidemembrane. ThehydrogenperoxideinitiatesformationofreactiveradicalssuchasHydroxyland hydroperoxylinpresenceofFe +3 ,Cu +2 ,etc.asfollows 81,83 H 2 O 2 +M +2 M +3 +OH +OH )]TJ/F15 11.9552 Tf 117.138 -4.936 Td [({11 H 2 O 2 +OH OOH +H 2 O{12 Toinvestigatetheformationoftheseradicalinthefuelcell,electronspinresonance ESRstudyhasbeenusedbyEndohetal. 84 Theyhavealsofoundthattheseradicals degradecatalystbyattackingcarbonincatalystlayer.Theseradicalsattackside-chain ofmembraneformingHFthereforeuorineemissionrateFERisproposedasan indicationofmembranedegradation. 81,9,85 However,peroxideconcentrationcannot bedirectlyrelatedtomembranedegradationbecausedegradationresultsfromaseries ofreactions:formationofperoxide,followedbyformationofradicals,nallyattack oftheseradicalsonside-chain.Also,formationofradicalsrequirepresenceofmetal ions. 78 Theseionsaretypicalcontaminationfrompiping,tubes,andstoragetanksof thefuelcell.Fe +3 canalsoarisefrombipolarplatecontamination. 69 FERrepresents materialerosionanddecompositionacrosstheoverallcellmaynotaccuratelyreect localdegradationofmembranewhichdependsonlocaltemperature,hydrationlevel, contaminationconcentration,etc. 86 Theformationofcross-linkingS )]TJ/F15 11.9552 Tf 11.955 0 Td [(O )]TJ/F15 11.9552 Tf 11.955 0 Td [(Sisreported whichcanbeduetodissolutionofacidicgroupofNaon )]TJ/F15 11.9552 Tf 9.298 0 Td [(SO 3 H ;pendentside-chain provokedbyperoxideleadingtodegradation. 87 Thelossofacidicsites,reductionin protonconductivityofmembranewasobserved. 40

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2.3.2PlatinumOxidationandDissolution Platinumdissolves 10 inthefuelcellenvironment,whichcanalsoleadstotheloss ofcatalyticactivityand,consequently,thedegradationoftheelectrodeofthefuelcell andhencelossinperformance. 88 Aschemefordissolutionofplatinumwassuggestedby Meyersetal. 10 asfollows. Pt+H 2 O PtO+2H + +2e )]TJ/F15 11.9552 Tf 128.964 -4.936 Td [({13 inwhichPtOisformed,followedbyachemicaldissolutionreaction PtO+2H + Pt +2 +H 2 O{14 TherststepleadstoformationofaprotectivelayerofPtOwhichreducesactivesurface areabyblockingreactionsites.Inthesecondstep,thePtOoxidedissolvestoformPt ionleadingtolossofcatalystparticles.Theformationoftheplatinumoxideissupposed tohaveanindirectinuenceontheORRatthecathodebychangingtheeectiverate constantforthereaction. AnotherschemeforPtOformationinpresenceofwater/oxygenwasadvocatedalong withdierentreactiveradicalswhichdegrademembrane,catalyst,andcatalystsupport usedinthefuelcell. 89 EectofhumidityonPtOformationwasreported;formationof PtOwasobservedeveninabsenceofoxygenatthecathode. 90 Theoxideformationwas proposedtofollow Pt+H 2 O Pt )]TJ/F15 11.9552 Tf 11.956 0 Td [(OH+H + +e )]TJ/F15 11.9552 Tf 123.124 -4.936 Td [({15 Pt )]TJ/F15 11.9552 Tf 11.955 0 Td [(OH PtO+H + +e )]TJ/F15 11.9552 Tf 137.087 -4.936 Td [({16 withalargeramountofPtOobservedatlowerhumidity. TheformationofPtO,andPtO 2 wasreportedtofollow. 91 Pt+H 2 O PtO+2H + +2e )]TJ/F15 11.9552 Tf 128.964 -4.936 Td [({17 41

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with E 0 =0 : 98 )]TJ/F15 11.9552 Tf 11.956 0 Td [(0 : 059pH2{18 and PtO+H 2 O PtO 2 +2H + +2e )]TJ/F15 11.9552 Tf 122.046 -4.936 Td [({19 with E 0 =1 : 05 )]TJ/F15 11.9552 Tf 11.956 0 Td [(0 : 059pH2{20 Ptdissolutioninathefuelcellconditionsunderpotentialcyclewasinvestigatedandthe solubilityofPtwaspresentedasafunctionofdierentfactorssuchastemperature,pH, andoxygenpartialpressure. 92 Thedissolutionreactionwasfoundtobeanexothermic reaction,andsolubilityofPtincreasedwithtemperature.Thesolubilityincreasewith decreaseinpHandsolubilitysignicantlyincreaseswithpresenceofoxygeninatmosphere accordingto: PtO+ 1 2 O 2 +2H + +H 2 O PtOH + 3 {21 ThenitesolubilityofPtinacidicmediumenablesitsmovementintoNaon.The movementofPtparticlescanbeaccomplishedbydiusion,migrationandpossiblyby convection. 93 Ptparticlesdissolveincatalystlayerandsubsequentaggregatedintobigger particlestheprocessisgovernbyOstwaldripening.Onceparticleshavegrownbiggerin micro-sizetheycanmigratebydiusionincatalystlayerand/orintomembrane. 94 Inside themembrane,themovementcanalsobeconsideredbyconvectionmode.Amathematical modelforPtmovementinmembraneisillustratedbasedondilute-solutiontheorythough ithasignoredseveralrealisticfactorssucheectofdouble-layercharging,convection BrownianmotionofPtparticles,andpotentialdependencyonthechargemovement. 95 Severalotherresearchershaveadvocatedplatinumoxidationanddissolutionunder normalthefuelcelloperatingconditions. 87,96{98,93,90,99 Experimentalresultshavealso conrmedcoarseningofthePtparticlesafter500hoursofoperation. 100 Theplatinum oxidationanddissolutionmayresultindecreasesofelectrochemicallyactivesurfacearea 42

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andhavealsoattributedtometalcatalystclusterformationor/andlossofthecatalyst support, 101 platinumdissolutionandredepositingatthecatalyst/electrolyteinterface, 100 andmigrationoftheplatinumparticlestothemembraneinterface. 94 Ptconcentrationincreasesmonotonicallyuntil1.1Vduetoformationofaprotective lmofPtObutafter1.1VPtOcandissolvetoformPtO 2 andsoadecreaseinPt concentrationispossible.ItisalsoreportedthatthisPtOhasnitesolubilitythatcan diuseleavingbarePtforfurtherformationofPtO. 97 Ptgrowthandaggregationis notfoundwhenAlwasusedasacatalystsupportusedinsteadofcarbon.Carbonwas proposedtohelpelectrontransferbetweensmallerandbiggerparticlesofPtwhich completesaggregation. 99 Ptwasobservedatcatalyst-membraneinterfaceduetomigration ofparticles, 96 isalsoreportedinsidethemembraneduetodiusionandredeposition.A bandofPtisreportedinsidethemembrane.Thelocationofthebandcanbecalculated byequatinguxesofhydrogenandoxygenfromrespectiveelectrodeswhichwasfurther validatedbySEM-TEM. 93 Otherfactorssuchascorrosionofcarbonsupport C+H 2 O CO 2 +4H + +4e )]TJ/F15 11.9552 Tf 130.661 -4.936 Td [({22 maycausepermanentlossofcatalystsupport,lossofcatalyticactivity,and,inextreme cases,astructuralcollapseoftheelectrolytemayleadtodegradationofthefuelcell. 11 Moredetailsofcarboncorrosionandcorrosionproductsatdierenttemperaturecanbe foundelsewhere. 102 Silicaisusedasagasketsealmaterialtoassemblethefuelcell.Itwasreported thatsiliconslowlyleachesanddepositsonthecatalyst;however,itdidnotdegrade thecatalyst.ThedepositedSiliconwasfoundtoblockoxygentransportduetoits hydrophobicity. 103 Presenceoftracesofvariousgasesasimpuritiesinthefuelhasalso beenreportedtohaveadetrimentaleectontheperformanceandlifetimeofthefuel cell. 104 43

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2.4ElectrochemicalImpedanceSpectroscopy Impedancespectroscopyisaveryusefuldiagnostictoolbecauseitisanon-invasive techniqueandcanprocureinformationabouttheprocessesinsidethefuelcell.Itisa powerfulcharacterizationtechniquewhichallowsseparatingdierentprocessesoccurring inthesystemdependingontimeconstantoftheprocessandcouldbeusedtostudycomplexsystemlikefuelcell.Impedancespectroscopy 105,64,106,107 isoftenusedtocharacterize processesinfuelcells.Theimpedancestudyhasbeenreportedtocharacterizesolidoxide fuelscellsSOFCs 108{113 andalsotocharacterizemethanolfuelcells. 114,115 Anextensive impedanceinvestigationforPEMFCshasbeenreportedinliterature. Springer etal 64 havereportedatypicalimpedanceresponseofthecathodeincludes twoarc,ahighfrequencyarcreectingthecombinationofaneectivechargetransfer resistanceandadouble-layercapacitanceinthecatalystlayerandalow-frequencyarc reectingmass-transportlimitationswithinthebackinglayer.Cirreanu etal. 107 have conductedrigorouskineticsstudyforthefuelcellbytheimpedancetechniques.Merida etal. 116 andLeCanut etal. 12 havedescribedtheuseofimpedancespectroscopyfor fuel-celldiagnostics.Lee etal. 60 usedimpedancetoevaluatetheoptimumNaonloading inthecatalystactivelayerCAL.Song etal. 61 usedimpedancetoevaluatetheoptimal compositionofthecatalystlayersupportmaterial.Cha etal. 117 studiedoodingofa microowchannel.EectsofrepetitivefreezingofwaterresidinginPEMFC,onthe characteristicsofthefuelcellwereinvestigatedbyCho. 118 Someresearchgroups 119{123 havealsousedtheimpedancetocharacterizeCOtoleranceofthefuelcell.Adescriptive reviewofliteraturerelatedtoimpedanceinvestigationsofvariousaspectsofthefuelcellis presentedinChapter3 Applicationofthistechniquetofuelcellshasbeenhamperedbecausetheexperiments arediculttoperformandarepronetoartifacts,andfundamentalinterpretationmodels arenotavailable.Thefuelcellsaresensitivetoanythinginsidethecell,soitisdicultto determineifdatafrominstrumentationinsidethecellisduetocellbehaviororduetothe 44

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artifactofinstrument.Themeasurementmodelwasusedtoanalyzepossibleerrorinthe impedanceresponseofthefuelcellwhichisdiscussedinChapter4. 2.4.1MeasurementModelAnalysis Themodelwasintroducedasameanstoresolverecurringissuesinregressionof impedancedata, e.g., 124{127 1.identicationofthemostappropriateweightingstrategyforregression, 2.assessmentofthenoiselevelinthemeasurement,and 3.identicationofthefrequencyrangeunaectedbyinstrumentalartifactsornonstationarybehavior. Theerrorsinanimpedancemeasurementcanbeexpressedintermsofthedierence betweentheobservedvalue Z andamodelvalue b Z as res = Z )]TJ/F27 11.9552 Tf 14.045 3.022 Td [(b Z = t + bias + stoch {23 where res representstheresidualerror, t isthesystematicerrorthatcanbeattributedtoinadequaciesofthemodel, bias representsthesystematicexperimentalbias errorthatcannotbeattributedtomodelinadequacies,and stoch isthestochasticerror withexpectation E f stoch g =0. Adistinctionisdrawn,followingAgarwal etal., 124{126 betweenstochasticerrorsthat arerandomlydistributedaboutameanvalueofzero,errorscausedbythelackoft ofamodel,andexperimentalbiaserrorsthatarepropagatedthroughthemodel.The experimentalbiaserrors,assumedtobethosethatcauselackofconsistencywiththe Kramers-Kronigrelations, 128{130 maybecausedbynonstationarityorbyinstrumental artifacts.Theproblemofinterpretationofimpedancedataisthereforedenedtoconsist oftwoparts:oneofidenticationofexperimentalerrors,whichincludesassessmentof consistencywiththeKramers-Kronigrelations,andoneoftting,whichentailsmodel identication,selectionofweightingstrategies,andexaminationofresidualerrors.The 45

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erroranalysisprovidesinformationthatcanbeincorporatedintoregressionofprocess models. Themeasurementmodelmethodfordistinguishingbetweenbiasandstochasticerrors isbasedonusingageneralizedmodelasalterfornon-replicacyofimpedancedata.The measurementmodeliscomposedofasuperpositionofline-shapeswhichcanbearbitrarily chosensubjecttotheconstraintthatthemodelsatisestheKramers-Kronigrelations. ThemodelcomposedofVoigtelementsinserieswithasolutionresistance, i.e., Z = R 0 + K X k =1 R k 1+ j! k {24 hasbeenshowntobeausefulmeasurementmodel.Withasucientnumberofparameters,theVoigtmodelwasabletoprovideastatisticallysignicantttoabroadvarietyof impedancespectra. 124 Themeasurementmodelisusedrsttolterlackofreplicationofrepeated impedancescans.Thestatisticsoftheresidualerrorsyieldsanestimateforthevariance orstandarddeviationofstochasticmeasurementerrors.Thisexperimentally-determined varianceisthenusedtoweightsubsequentregressionofthemeasurementmodeltodetermineconsistencywiththeKramers-Kronigrelations.Ifthedatacanberepresentedby amodelthatisitselfconsistentwiththeKramers-Kronigrelations,thedatacanbeconsideredtobeconsistent.Theconceptofusingageneralizedmeasurementmodeltoassess consistencywiththeKramers-Kronigrelations,rstintroducedbyAgarwal etal., 124,126,131 wasalsoemployedbyBoukampandMacdonald 132 andbyBoukamp 133 usingweighting strategiesbasedonanassumederrorstructure.Theexperimentaldeterminationofthe stochasticerrorstructureasusedhere,however,allowsformalquanticationoftheextent ofagreementwiththeKramers-Kronigrelations. Othertransfer-functionmodelscanbeusedasameasurementmodelsolongasthey areconsistentwiththeKramers-Kronigrelations.ShuklaandOrazemhavedemonstrated thatthestochasticerrorstructuredeterminedfromreplicatedimpedancemeasurementsis 46

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independentofthetypeofmeasurementmodelused. 134 Whiletheregressedparameters maynotbeassociatedunequivocallywithasetofdeterministicortheoreticalparameters foragivensystem,themeasurementmodelapproachhasbeenshowntorepresentadequatelytheimpedancespectraobtainedforalargevarietyofelectrochemicalsystems. 124 Regardlessoftheirinterpretation,themeasurementmodelrepresentationcanbeusedto lterandthusidentifythenon-stationarydriftandhigh-frequencynoisecomponents containedinanimpedancespectrum. Themeasurementmodelhasbeenappliedinpreviousworktoassesstheerrorstructureofavarietyofsystemsincludingelectrohydrodynamicimpedance, 135 electrochemical impedancedataforreductionofferricyanideonaPtrotatingdisk, 136 forcorrosionofcast ironinEvianwater, 137 forcorrosionofaluminuminorangejuice, 127 andforchargingof electroactivepolymers. 138 2.4.2InterpretationModel Mathematicalmodelsareneededtointerprettheimpedancedata,includingthe low-frequencyinductiveloops,intermsofphysicalprocesses.Gomadam etal. 139 have reportedanexclusivereviewofimportantliteraturefordierentapproachestomodel theimpedanceresponseofthefuelcellandhavealsopresentedaconcisecomparisonof continuum-mechanics-basedandequivalent-circuitbasedapproachmodeling.Themost quantitativeoftheimpedancemodelsreportedintheliteraturehaveemphasizeddetailed treatmentofthetransportprocesses,butuseofsimpleelectrochemicalmechanisms precludedpredictionoftheinductiveloops.AstheoxygenreductionreactionORRat thecathodeistherate-determiningstep,mostmodelsemphasizethereactionkinetics atthecathode.Theone-dimensionalmodelsproposedbySpringer etal. 64,140 considered thecathodetobeathinlmonagglomeratedcatalystparticles.Theystudiedtheroleof wateraccumulationinthegasdiusionlayerandoxygendiusioninthegasphase.These modelsconsideredonlyasingle-stepirreversibleORRatthecathode.Theimpedance modelsbyotherresearchers 141{143 alsotreatedasingle-stepkineticsfortheORR. 47

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SeveralmodelsfortheimpedanceresponseofPEMfuelcellshaveconsidereda moredetailedreactionmechanism.ThemodeldevelopedbyEikerlingandKornyshev 19 consideredasingle-stepORRtobereversibleatthecathode.Antoine etal. 144 has proposedanimpedancemodelwithathree-stepORRkineticsinacidicmediumon platinumnanoparticlesthoughreactionintermediateswereunspeciedandkineticsat theanodewasnotconsideredintheirmodel.Theyexplainedthatthelow-frequency inductiveloopswerearesultofthesecondrelaxationoftheadsorbedspeciesinvolved inthedierentstepsoftheORR.Morerecently,Wiezell etal. 145 consideredatwo-step hydrogenoxidationreactionHORandhavereportedlow-frequencyinductiveloops. Theyexplainedthattheinductiveloopsweretheresultofchangingfactorssuchaswater concentration,membranethickness,hydrogenpressureandtheHORkinetics. TheroleofintermediatesintheORRissupportedbyindependentobservation ofhydrogenperoxideformationinPEMfuelcells. 7{9 Arotating-ring-disk-electrode study 77 revealedthatformationoftheperoxideonplatinumparticlessupportedon carboncatalystusedinthefuelcellisquitepossiblebytwo-electronreductionwhile theformationisnotanoptiononcleanbulkplatinum.Thehydrogenperoxideformed asanintermediatecauseschemicaldegradationofthemembrane. 9 Otherreactions havealsobeenreportedwhichcouldpotentiallyaccountforthelow-frequencyfeatures observedintheimpedancedata.Platinumdissolution,forexample,hasbeenobservedin PEMfuelcells 10 whichcanleadtothelossofcatalyticactivityand,consequently,tothe degradationofthefuelcellperformance. 88 Sidereactionsandtheassociatedintermediates candegradefuelcellcomponentssuchasmembranesandelectrodes,therebyreducingthe lifetime,oneofthecrucialissuesinthecommercializationoffuelcells. 146 Theinuence ofsidereactionsandreactionintermediatesontheimpedanceresponseiscomparatively unexplored. 48

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2.4.3FloodingintheFuelCell Theperformanceofthefuelcellisinuencedbykineticlimitationsatlowcurrent densities,Ohmiclimitationsatintermediatecurrentdensities,andmass-transferlimitationsathighcurrentdensities.Kulikovsky 147 andBerg etal. 148 havedescribedindetail thecriticalroleofwatermanagementinoperationofthefuelcell.Tomaintainproton conductivity,thefuelcellmembranemustremainhydrated.Toachievehydration,the relativehumidityofinletgassesistypicallyheldatalargevalue.Water,however,isalso aproductofthecathodicreaction;thus,anexcessofwaterinthecathodeiscommonly observed,whichcanleadtocondensationandsubsequentooding.Floodingincreasesthe resistanceassociatedwiththegasdiusionlayerandmayevenblockowchannels,reducingtheavailabilityofoxygen. 149 Condensedwatermayberemovedbygasow.Thus, changesindesignofreactantowchannelsandgasdiusionlayershavebeenproposedto reducetheinuenceofooding. Pressuredrophasbeenreportedtoprovideasuitablediagnostictoolformonitoring oodinginthefuelcell. 150 Floodingwasalsoinvestigatedbycorrelatingtheappearance ofoodingtotheFaradaicresistance. 151 Barbir etal. 152 haveinvestigatedtherelationship betweenpressuredropandcellresistancetomakeadistinctionbetweenoodingand drying.Theyobservedthatbothpressuredropandcellresistancechangedincaseof drying;whereas,onlypressuredropchangedunderoodingconditions.Ge etal. 153 observedthattheanodeoodingismainlyduetowater-dropletcondensationatchannel wallsincontrasttooodingatthecathodewhichisusuallyattributedtocondensation ingasdiusionlayerGDL.TheyhavealsoreportedthatuseofahydrophilicGDLand elevatedanodeplatetemperaturecouldmitigateanodeooding.Theonsetofooding maybeseeninsteady-statemeasurements,buttheimpedanceresponseisevenmore sensitivetoappearanceofoodingconditions.Theimpedancetechniquehasrecently beenusedtodetectmembranedrying,ooding,andanodepoisoningoffuelcellstacks. 12 Merida etal. 116 havealsoinvestigatedfailuremodesdryingandoodingofthefuel 49

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cellusingtheimpedancetechnique.TheapproachtakenbyLeCanut etal. 12 andMerida etal. 116 wastodetectoodingbyobservingincreasesinthevalueoftheimpedance ascomparedtoanormalimpedancemeasuredatthebeginningofcelloperation.The advantageoftheirapproachisthataphysicalmodelisnotneeded.Thedicultieswith normalizingtheimpedancetotheimpedancemeasuredatthebeginningofcelloperation arethatsteady-stateoperationwillgenerallynotbeestablishedduringthismeasurement, thattheremaybeotherreasonsforincreasesincellimpedancewithtime,andthat oodingmayalreadybetakingplaceduringtheinitialmeasurement. Locally-resolvedimpedancespectroscopyandNMRimaginghavebeenusedto investigateoodinganddryinginthefuelcellbySchneider etal. 154{156 Theauthors reportedthat,forco-owcongurations,membranedryingwasevidentnearthegas inletandoodingwasseverenearthegasoutlet. 155 Theauthorshavealsoreported thatdryingandoodingweremorepronouncedinco-owascomparedtocounter-ow congurations. 156 Fouquet etal. 157 ttedaRandles-likeequivalentcircuittoimpedance dataandcorrelatedcircuitvaluestothestate-of-healthoodinganddryingofthefuel cell.TheRandles-likecircuit,however,cannotaccountforallthephenomenatakingplace inthefuelcell.Whiletherearedierencesinthespecicapproachestaken,theunderlying conceptforeachoftheseapproacheswasthatonecandetectoodingbyobserving increasesinthevalueoftheimpedance. 2.4.4EvaluationofInterfacialCapacitance ElectricalcircuitsinvokingConstant-PhaseElementsCPEareoftenusedto timpedancedatabecausetheassociateddistributionoftimeconstantsprovidesan improvedt. 158{160 Thedistributionoftimeconstantshasbeenattributedtosurface heterogeneity 161,162 ortocontinuouslydistributedtimeconstantsforcharge-transfer reactions. 163{167 TheCPEparametersmaygiveinsightintosurfacedisorderandsurface roughness, 168 electrodeporosity, 169 andnon-uniformpotentialandcurrentdistribution. 170,171 50

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ElectricalcircuitsinvokingCPEshavebeenusedtomodeltheimpedanceresponseof PEMfuelcells.Ciureanu etal. 106 usedtheimpedancetechniquetostudytheoxidation ofhydrogenandhydrogen-COmixtureinafuelcellandttedtheresultusingCPE parameters.TheeectofCOontheperformanceofthefuelcellhasbeenreportedby impedancetechniqueandtheimpedanceresponsehasbeenttedusingCPEparameters toillustratephysicalprocesses. 120 TheCPEparametershavealsobeenusedtotthe impedanceresponseofelectrocatalystsfortheanodeofthefuelcell. 172 Meland etal. 173 studiedeectofwaterontheanodereactioninthefuelcellbyimpedanceandhavetted impedanceresponseusingtheCPEparameters,havereportedparametersasafunction ofoperatingpotential.TheCPEparametershavebeenusedtomodelimpedancestudy forcharacterizingdierentmethodsforcatalyticinkpreparationforthefuelcell. 174 TheCPEapproachhasalsobeenexploitedtocharacterizecarbon-nanotube-supported electrocatalytsforanodes, 175 tostudyanodematerialsforthesolidoxidefuelcells, 176 andtomodeltheimpedanceresponseoftheporousanodeofamethanolfuelcell. 177 ThedepressedsemicircleseeninNyquistplotshasbeenattributedtonon-homogeneity ofelectrodesurface. 178 Fouquet etal. 157 haveattemptedtocorrelateparameterstothe state-of-healthoodinganddryingofaPEMfuelcellthoughtheparameterswereagain estimatedbyttingimpedancedata.Theinterfacialcapacitancewasestimatedemploying graphicalmethodstointerpretimpedanceresponseintermofphysicalprocessessuch oodinganddryingwhichistobesubmittedasatechnicalarticle. 179 51

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CHAPTER3 EXPERIMENTAL Detailsofexperimentalmethodsandmaterialsaredescribedinthischapter. Impedanceandpolarizationdatacollectedonthefuelcellarepresentedanddiscussed.A concisereviewofliteraturerelatedtoexperimentalinvestigationsofvariousaspectsofthe fuelcellsuchasreactionkinetics,transportmechanisms,performanceandlifetimeanalysis hasalsobeenoutlined. 3.1Introduction Impedancespectroscopyisoftenusedtocharacterizeprocessesinfuelcells,including PEMfuelcells. 64,105{108 Springer etal 64 havereportedatypicalimpedanceresponseof thecathodeforthefuelcellwhichincludestwoarcs,ahighfrequencyarcreectingthe combinationofaneectivechargetransferresistanceandadouble-layercapacitancein thecatalystlayerandalow-frequencyarcreectingmass-transportlimitationswithin thebackinglayer.Thestraight-lineportioninthehighfrequencyarcisattributedto distributedionicresistanceanddistributedcapacitanceinthecatalystlayer.Paganin et al. 65 usedimpedancespectroscopytostudytheeectofcelltemperature,oxygenpartial pressure,electrodecomposition,andmembranethicknessonthefuelcellperformance. Andreaus etal. 180 usedimpedancedataobtainedunderhighcurrentdensitiestoestimate performancelossesinthefuelcell.Theyusedmembraneswithdierentthicknessand ionicdensityequivalentweighttoprovethatloopatlowfrequencyinimpedance responsecanalsobeduetoanodedryingoutwhichleadtolowprotonmobilityin additiontooxygentransportlimitedbyooding.Ciureanu 181 hasexaminedtheohmic resistanceofNaonmembranesasfunctionofhumidicationconditionsforlowcurrent density-400mA/cm 2 .Forwell-humidiedcathode,theyhavereportedthatthe resistancewassmallandrelativelyconstanttothepresenceoftheanodichumidication whilefornon-humidiedcathodesthemembraneresistancewashighandstrongly dependentoncurrentandanodichumidication.DehydrationoftheNaonpresentinthe cathodecatalyticlayerresultedinanincreaseofthepolarizationresistanceinaddition 52

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totheohmicresistanceofthemembrane;theapparentdeactivationofthecathode electrocatalystappearstobeduetoadecreaseoftheelectrochemicallyactivesurfacearea. Lee etal. 60 usedimpedancetoevaluatetheoptimumNaonloadingintheCAL. Song etal. 61 usedimpedancetoevaluatetheoptimalcompositionofthecatalystsupport material.ThestudyconductedbyHombrados etal. 182 hasdiscussedimpedancemeasurementsforkineticsanalysisofboththecathodeandtheanodereactionmechanisms.They havesuggestedaequivalent-circuitmodeltottheimpedancedata,andhaveevaluated parameterssuchasmembraneconductivity,andchargetransferresistanceasafunctionof operatingconditionslikehumidicationtemperature,andreactantowrate.Three-step hydrogenkineticsconsistingofdiusion-adsorptionofhydrogenmolecule,formationof proton,andprotonhydrationcombinationofprotonwithwaterisproposedbyMeland etal. 173 Theyndtheprotonhydrationasarate-determiningstepathighertemperature whereduetolessamountofwatertimeconstantforthisstepbecomeslargerandtherefore collapsedintohighfrequencyarc.Abe etal. 183 usedimpedancetoanalyzetheeectof humidityintheoxygenstreamatthecathodeofthefuelcell.Lefebvre etal. 58 haveused theimpedancetocharacterizeproton-conductingandelectron-conductingpolymerparticlesforcatalystsupportforfuelcells.Theyevaluatedcatalyticactivitiesofthecatalyst supporttowardhydrogenandmethanoloxidationandoxygenreductioninthefuel-celltypegasdiusionelectrodes.Theyhavereportedthattheactivitiesforoxygenreduction comparabletothatobtainedwithacommercialcarbon-supportedcatalystwereobserved, whereasthoseforhydrogenandmethanoloxidationweresignicantlyinferior,although stillhighforprototypecatalysts.ThepreparationandthefuelcellevaluationofsPSU basedMEAsatvaryingtemperatureswasinvestigatedbyKraemer etal. 184 Theyhave reportedthattheMEAhaslowresistancethoughitshowedmasstransportlimitations intherangeof600-800mA/cm 2 ,mostprobablycausedbyabundantwaterduetothe overhumidiedmeasuringconditions. 53

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Paganin etal 65 havereportedonearcandhaveexplainedthelow-frequencyarchas beensuperimposedonthehigher-frequencyarc.Theoverallimpedanceresponsehasbeen explainedastheeectofthedouble-layercapacitanceandthechargetransferresistance ofoxygenreductionreactionORR.Song etal. 61 havereportedtwocapacitiveloops fortheimpedanceresponseofthefuelcell.ImpedanceresponsereportedbySpringer et al 64 includestwoarcs.ThestudyconductedbyCirreanu etal. 185 hasinvestigatedthe impedanceresponseofthefuelcellwithdierentcellvoltage,humidicationtemperature ofreactants,andairowrate.Theyhavereportedimpedancespectrawithtwoloops: thehigh-frequencyloopwasattributedtotheeectofreactionkineticsandoxygen transportintheCAL,andthelow-frequencyloopwasattributedtomasstransport limitationsofgasesandwaterintheGDL.Thegrouphasalsosuggestedacircuitanalog modeltoexplaintheexperimentalresultsandhavecalculatedtheparameterssuchas surfaceexchangecurrentdensityandTafelslopes.Manyauthors e.g., Castan~na etal. 186 andLi etal., 62 reportedonlyonecapacitiveloop.Castanna etal 186 havereportedan exponentialdecreaseinthechargetransferresistancewithincreasesintheoverpotential. Theyalsohavereportedthedecreasesinthedouble-layercapacitancewiththeincreases intheoverpotentialandthecapacitancereachesaconstantvalueoncetheperformanceis controlledbyohmiceects.Thehighervalueofthecapacitanceobservedinthekinetics controlregioncouldbeduetocharging-dischargingprocessesintheregion. Someresearchgroups 119{123 havealsousedtheimpedancetocharacterizeCOtoleranceofthefuelcell.Jiang etal. 119 havereportedtheimpedancestudytocharacterizeCO toleranceofelectrocatalystasafunctionofDCbiaspotential,temperatureandrelative humiditywhileKim etal. 120 haveusedtheimpedancetoinvestigatetheeectofCO ontheperformanceofthefuelcellandhavereportedthatcharge-transferresistanceas wellashydrogendissociationresistanceincreasewithanincreaseintheCOconcentrationbutithaslittleeectonlowfrequencyarcoftheimpedancespectra.Yang etal. 121 haveappliedathree-electrodearrangementtoinvestigateeectoftheCOonthefuel 54

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cellperformance.Theyhavereportedthattheoverpotentialofanodeinpresenceofthe COincreasesduetoincreaseinbothcharge-transferresistanceandohmicresistancein thecatalystlayer.Mazurek etal. 123 haveconductedtheimpedancestudytocharacterizetheCOtoleranceofcarbon-supportedPtandcarbon-supportedRufortheanode electrocatalyst.Theyhavereportedthatthecarbon-supportedRucatalysthavebetter catalyticactivitythanthePtandalsothesmallerparticlesizeofRubetterperformance wasobserved. Theinuenceofcarbonmonoxidepoisoningontheplatinumandplatinum-ruthenium anodewasinvestigatedbyWagnerandSchulze 187 usingtheimpedancespectroscopy.They foundthatthedegradationofthefuelcellperformanceduringthepoisoningwithCO wasdominatedbyanincreaseofanodicchargetransferresistancesandanincreaseof thenitediusionimpedance.Theyhavealsoobservedthatimpedancespectraexhibit pseudo-inductivecontributionsatthelowfrequencypartofthespectra,whichincrease duringtheexperiment.Theincreasingpseudo-inductivebehaviorhasbeenexplained becauseofasurfacerelaxationprocessduetothecompetitiveoxidationofhydrogenand carbonmonoxideattheanode.Cirreanu etal. 107 haveconductedrigorouskineticsstudy forthefuelcellbytheimpedancetechniques.Theyhavealsoreportedtheeectofcarbon monoxideontheanodekinetics,andthefuelcellperformance.Theinuenceofcarbon monoxidepoisoningonplatinumandplatinum-rutheniumanodeswasinvestigatedusing impedancespectroscopy. 187,188 Impedanceinvestigationshavealsobeenreportedfordierentfuelcellapplicationssuchasstudiesoftheeectofmembranethicknessontheconductivityofthe Naon, 189 characterizationofelectrosprayedNaonlms, 190 performanceevaluationof self-humidiedcompositemembranes, 191 andcharacterizationofsingle-walledcarbonnanotube-basedprotonexchangemembraneassembliesforhydrogenfuelcells. 52 Ithas alsobeenusedtostudyionexchangecapacityofcompositemembranesforhightemperatureapplications, 30 todetermineconductivityofcompositemembranesforintermediate 55

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temperaturefuel-cellapplications, 34 tostudytheeectoftemperatureonresistance andprotonconductivityofcompositemembranes, 35,36 tomeasureionicandelectronic resistibilityofcompositeelectrodecatalystforthefuelcellapplication. 37 Usingthe impedance,Li etal. 115 haveinvestigatedareferenceelectrodetoresolveeectsatthe anodeandcathodeandwithinthemembranethefuelcell. Theobjectofthischapteristoprovideacomprehensiveanalysisofperformanceof thefuelcellintermsofimpedanceandpolarizationresultsasafunctionofseveralfactors. Thefactorsanalyzedincludeoperatingconditionssuchascurrentdensity,temperature, andbackpressure,anddesignparameterssuchasowchannels,andGDLs.Briefof techniques,methods,andmaterialsusedisalsopresented. 3.2Experimental Theexperimentalsystemandtheimpedanceinstrumentationusedarepresentedin thissection. 3.2.1MaterialsandChemicals TheMEApurchasedfromIonPower,Inc.,NewCastle,DEemployed0.0508mm milsthickNaonN112withcatalystlayersofabout0.025mmonbothsidesofthe membrane.Theactivesurfaceareawas5cm 2 .OnemoreMEAwiththesamethicknessof themembrane,andcatalystbutembededGDLbothsideofthecatalystlayerswasused whichwassuppliedbyfuelcellstoreSanDiego,CA.Thecatalystlayerswereplatinum supportedoncarbonwithaPtcatalystloadingof0.4mg/cm 2 onboththeanodeand thecathodesides.TwotypesofGDLwereusedduringassemblingtheMEA.Both haveaneectivethicknessof0.284mm,andweremadeofcarboncloth,butonewas uniformlymacro-porouswhiletheotherhasvariableporosity.ThenonuniformGDLwas micro-poroustothecatalystsideandmacro-poroustothechannelside.SimilarGDL structureshavebeenreportedintheliterature. 64{66 Thematerialoftheowchannel owcongurationsareshowninFigure3-1usedwasmadeofgraphitewiththeoutlet lowerthantheinlettofacilitateremovalofcondensedwater.Hydrogengaswasusedas 56

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a b Figure3-1:Thecongurationsofowchannels; 4 aserpentine;andbinterdigitated. fuelandcompressedairwasusedasoxidant.CompressedN 2 wasusedforpurgingofthe fuelcellbeforeandafterexperiments.ABarnsteadE-PureWaterSystemwithanion resistivityof14.9 M c m wasusedasasourceofdeionizedwaterdeliveredtotheanode andthecathodehumidiers. An850Cfuel-cellteststationsuppliedbyScribnerAssociates,SouthernPines,NC wasusedtocontrolreactantowratesandtemperatures.Theteststationwasconnected toacomputerbyaninterfacefordataacquisition.Thegasowtotheanodewasheldat temperatureof40 0 : 1 C,andthegasowtothethecathodewasheldatatemperature of35 0 : 1 C.Thegasowswerehumidiedto100percentrelativehumidityatthe respectivetemperatures.Thecelltemperaturewasheldat40 0 : 1 C.Thehydrogen owratewas0.1liters/minandtheairowratewas0.5liters/min.Themaximum stoichiometryforhydrogenandairwas1.5and2.5,respectively,andthecellwasoperated atthefully-humidiedcondition. 57

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3.2.2ElectrochemicalImpedanceMeasurements Impedancemeasurementswereperformedusingtwodierentsystems.TheScribner Associates850CFuelCellTestStandcontainsbothanelectronicloadandafrequency responseanalyzer.Impedancemeasurementsobtainedwiththe850Cwerecomparedto impedancecollectedusingaGamryInstrumentsFC350impedanceanalyzercoupledwith aDynaloadelectronicloadRBL100V-60A-400W.Allelectrochemicalmeasurementswere performedwithatwo-electrodecellinwhichtheanodewasusedasapseudo-reference electrode. TheprotocolrecommendedbyRamani etal. 192 wasusedtoensurethatthesystem reachedsteady-stateoperationbeforeimpedancemeasurementsweretaken.Theprotocol consistedoftwosteps: 1.Uponstartup,thecurrentwassweptfromzerotothemaximumvalueinforward andreversedirectionsuntilhysteresisinthepolarizationcurvewasnolonger evident.ThisprocedurewasintendedtoensurecompletehydrationoftheMEA. Thissteprequiredupto48hoursbreak-intimeforanewMEAand1.5hoursfor asystemthathadbeenrecentlyused. 2.Oncethehysteresisinthepolarizationcurvewasnolongerevident,thecurrentwas setandthepotentialwasmonitored.Impedancemeasurementswereconductedafter thepotentialwasstabilized.Thissteprequired30minutes. Thepolarizationcurveswereobtainedbysteppingthecurrentfromzerotothe maximumcurrentwithanincrementof10mA/30sec.Atypicalpolarizationcurvesis presentedinFigure3-2. Repeatedimpedancemeasurementswereperformedatseveralpointsonthepolarizationcurve.Theimpedancemeasurementswereconductedingalavanostaticmodefor frequencyrangeof3kHzto1mHzwitha10mApeak-to-peaksinusoidalperturbation. Thecorrespondingpotentialperturbationrangedfrom0.04mVathighfrequencyto0.4 mVatlowfrequency.Thefrequencieswerespacedinlogarithmicprogressionwith10 58

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pointsperfrequencydecade.Impedancescanswereconductedinauto-integrationmode withaminimumof2cyclesperfrequencymeasured.Eachscanrequired5hoursfor theScribnersystemand3hoursfortheGamrysystem.Thedierenceintimerequired canbeattributedtodierencesinimpedancesettings.Thelongtimerequiredatlower frequenciesmademeasurementsatthesefrequenciessusceptibletobeinginuencedby nonstationarybehavior. 3.2.3OtherElectrochemicalTechniques LinearsweepvoltammetryLSV 31,32 wasperformedtomeasurethehydrogen crossoverthroughthemembrane.Inthisexperiment,thefuelcellwaspolarizedina potentialrangeof0to+0.4Vinwhichallhydrogenpresentisassumedtobeoxidized. Thefuel-cellteststationwasusedforbasiccontrolofowrateandtemperatureof reactantgases,andthevoltagescanwasconductedwithaSolaratron1286Potentiostat, whichwascoupledwiththeteststation.Theexperimentwasperformedinthetwoelectrodecongurationinwhichtheanodewastreatedasareferenceandthecathodewas treatedasaworkingelectrode.inductivelycoupledplasma-massspectroscopyICP-MS wasappliedtoestimatetheplatinumconcentration 94 intheoutletwaterofthecathodeof thefuelcell. Cyclicvoltammetrywasconductedtoevaluatetheelectrochemicallyactivesurface area 101,142,31 ofthecatalyst.TheexperimentalsetupdiscussedfortheLSVwasusedfor thisexperiment.Inthisexperiment,thefuelcellpotentialwassweptbothinforward directionto0.8Vandtheninreversedirection.8to0V.Resultsfromthese techniquesrelevanttothisworkispresentedinChapter5. 3.2.4SurfaceAnalysis Severalmicrostructuralcharacterizationstechniqueswereemployedtostudythe morphology,agglomeration,andoxidationstateofelementsinthecatalystandthe membraneoftheMEA.Detailsoftechniquesusedarepresentedinfollowingsection thoughtheresultsobtainedaredescribedinChapter5. 59

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3.2.4.1Scanningelectronmicroscope ThesurfacecharacteristicoftheMEAwasstudiedwiththescanningelectron microscopeSEM. 101,31 Forsamplepreparation,asmallportionfromthecenterofthe bothfreshandusedMEAwascutwithsharprazorandtheSEMimagesweretakenwith theJOELJSM6400availableatMAICintheUniversityofFlorida. 3.2.4.2Transmissionelectronmicroscope TheTEMwasusedforatomic-scalemicro-structuralandchemicalcharacterization oftheMEA. 100,94,33 Forsamplepreparation,asmallportionfromthecenterofthe bothfreshandusedMEAwascutwithsharprazorandwasembeddedonepoxyresin Araldite5002for48hoursat60 C.Thinnmsectionsfromthemembrane-electrodes interfaceswerecutwithadiamondknifeonReichertOMU3ultramicrotomeatroom temperature.ThesamplesweremountedonCugridmeshsize200priortoTEMstudy. Moredetailsonsamplepreparationcanbefoundelsewhere. 193 TEMstudywasperformed withaJOELJSM-2010FFieldEmissionElectronMicroscopeavailableatMAICinthe UniversityofFlorida,whichisequippedwithanenergydispersivespectrometerEDSfor compositionalanalysis.TheTEMmicrographsweretakenat200kVacceleratingvoltage forseveralmagnicationsinbrighteldmodetransmittedelectrons. 3.2.4.3X-rayphotoelectronspectroscopy TheXPSwasusedtoinspectpossibleelementsandcompoundsatthesurface15atomiclayersoftheMEA.Forsamplepreparation,asmallportioncmX1cmof thicknessequivalenttoMEAfromthecenterofthebothfreshandusedMEAwascut withsharprazorandtheXPSscansweretakenwiththePHI5100ESCAsystemby Perkin-ElmeravailableatMAICintheUniversityofFlorida.X-raysourcewasMganode withaworkfunction4.8eV.Theemittedelectronswerecollectedat45 0 withrespect tothesample.Thesamplewasscannedat300wattspowerinenergyrangeof1000-0 eVbindingenergywithastepof0.5eVand30mSec/step.Thesurveyfullscanwas generatedatpassenergy89.45eVwhereasnarrowscanshighresolutionforseveral 60

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Figure3-2:Polarizationcurvesrecordedwiththe850Cforaninterdigitatedchannelasa functionofcurrentdensitiesatthecelltemperature40 C.Theanodeandthecelltemperaturesweresetat40 Candthecathodetemperatureat35 C. peakswereperformedatpassenergyof22.36eV.Theatomswereassignedaccordingto bindingenergyofvisiblepeaksandatomiccompositionofelementswereevaluatedby relativesintensitiesofthepeaks. 3.3Results Steady-statemeasurementspolarizationcurvesandimpedanceresponsesofthefuel cellarepresentedasafunctionofdierentoperatingparameters. 3.3.1CurrentDensityasaParameter Impedancemeasurementswereperformedatseveralpointsalongthepolarization curvepresentedinFigure3-2.Twodierenttrendsintheimpedanceresponsewere observed.AsshowninFigure3-3,theimpedancedecreasedwithincreasingcurrent densityforlowcurrentdensity i< 0 : 5A/cm 2 .AsshowninFigure3-3,theimpedance increasedwithincreasingcurrentdensityforhighcurrentdensity i> 0 : 5A/cm 2 .These trendsareconsistentwithchangesintheslopeofthepolarizationcurvewithcurrent density.Itwasfoundthattheimpedancewasthelowestincaseofintermediatecurrent followedbythelowercurrentandtheimpedancewasfoundthehighestatthehigher currentofthefuelcell,whichwasconsistentwithourpreviousndings. 194 61

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Figure3-3:Impedanceresponsescollectedwiththe850Cforaninterdigitatedchannel asafunctionofcurrentdensitiesatthecelltemperature40 C.Theanodeandthecell temperaturesweresetat40 Candthecathodetemperatureat35 C. 3.3.2TemperatureasaParameter TheperformanceofthefuelcellasfunctionofthecelltemperaturewithaninterdigitatedowchannelwasinvestigatedandispresentedinFigure3-4.Anincreaseinthe performancewasobservedwithanincreaseinthecelltemperature.Protonconductivity ofthemembraneincreaseswithtemperature,othertransportpropertiessuchasdiusivity,electroosmoticcoecientalsoincreasewithtemperature,whichcouldenhancethe performanceatelevatedtemperatures. 3,195 Theincreaseintheperformanceforthecell temperatureisalsoexplainedastheenhancedreactionrateduetoincreasedtemperature. 4 TheimpedanceresponsedecreasedwiththetemperatureasshowninFigure3-5, whichsupportedthebetterperformancewithanincreaseinthetemperature. 3.3.3BackpressureasaParameter Polarizationcurvesandimpedancemeasurementswereobtainedasfunctionsof thebackpressureappliedontheanodeandcathode.Polarizationcurvesgeneratedasa functionofappliedbackpressureispresentedinFigure3-6a.AsevidentinFigure3-6a, theeectoftheBPcanbeespeciallydiscernedathighercurrentdensitiesmass-transfer region.ItwasobservedthattheperformanceimprovesbyincreasingBPfrom30to40 62

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Figure3-4:Polarizationcurvesrecordedasafunctionofcelltemperaturebythesteady statemeasurementwiththe850CforH 2 asreactantattheanodeandairasoxidantat thecathode.Theanodethecathodetemperatureatwerexedat70 C.Thefuelcellwas assembledwithaserpentinechannel. Figure3-5:Impedanceresponsesasafunctionoftemperatureat0.5A/cm 2 collectedwith the850Cwithaserpentinechannel. 63

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a b Figure3-6:Cellperformanceasafunctionofbackpressure.Themeasurementswereconductedwith850CforH 2 asreactantattheanodeandairasoxidantatcathode.The anodereactantstreamandcelltemperaturesweresetat60 0 Candthecathodereactant streamtemperatureat55 0 C.Thefuelcellwasassembledwithaserpentinechannel;a polarizationcurvegeneratedfromthesteady-statemeasurement;andbimpedanceresponserecordedat0.1A/cm 2 psi,butwhenBPwasincreasedfurtherfrom40to50psiadecreaseintheperformance wasrecorded. Toexplorefurther,theimpedanceresponsesasafunctionofappliedbackpressure weremeasuredatseveralsteady-statepointsonthepolarizationcurve.Impedanceresponserecordedat0.1A/cm 2 ,0.2A/cm 2 ,and0.4A/cm 2 arepresentedinFigures3-6b, 3-7a,and3-7brespectively.Thesecurrentdensitieswerechosentoberepresentative ofthekinetic,ohmic,andmass-transfercontrolledregionsofthepolarizationcurve.It wasobservedthattheappliedBPhasnoeectontheimpedanceresponserecordedin kineticregionasseeninFigure3-6bbuttheimpedanceresponsesatotherregions wereaectedbytheappliedbackpressure.Itwasdiscernedthattheimpedancedecreased betterperformanceastheBPwasincreasedfrom30to40psibut,asitwasincreased to50from40,therewasanincreaseintheimpedance,whichsuggestedthattherecould aoptimumbackpressureforcellperformance.TheeectoftheBPwasnotobservedin Ohmicregiononthepolarizationcurves,but,onthecorrespondingimpedancespectrathe eectwasevident. 64

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a b Figure3-7:Cellperformanceasafunctionofbackpressure.Themeasurementswereconductedwith850CforH 2 asreactantattheanodeandairasoxidantatcathode.The anodereactantstreamandcelltemperaturesweresetat60 0 Candthecathodereactant streamtemperatureat55 0 C.Thefuelcellwasassembledwithaserpentinechannel;a impedanceresponserecordedat0.2A/cm 2 ;andbimpedanceresponserecordedat0.4 A/cm 2 Backpressureconcentratesreactantsattheelectrode,whichcouldaectphysical propertiessuchaslocalsurfacetensionleadingtohighercapillaryriseandthusbetter transportofreactants. 196 However,athigherbackpressuretheperformancewouldcontrolledbyelectrodekineticsresultinginnoenhancementofcellperformance.Inaddition, reactantcrossoversuchasofhydrogenhasbeenreportedatenhancedbackpressure, 197 whichcanreducetheperformanceofthecell. 3.3.4HysteresisBehaviorandImpedanceResponse Galvanodynamiccurvesweremeasuredinforwardandreversedirections.Theforwardandreversedirectionsoftheresultinghysteresiscurvesaredenedintheliterature tobethewater-imbibitionandthewater-drainagecycles,respectively. 198 Ahysteresis curveobtainedat40 Cforascanrateof50mA/30sispresentedinFigure3-8a.Inthe hysteresiscurve,theforwardandbackwardscandirectionswerenotdistinguishablefor highercurrentdensitiesduetomultiplecrossingofwater-imbibitionandwater-drainage cycles.Themultiplecrossingofthetwocyclescouldbeattributedtorandommovementof water-droplets,whichcharacterizesoodingtobeastochasticprocess.Azoomedpicture oftheoodingregionhighcurrentdensityisshowninFigure3-8b. 65

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a b Figure3-8:Galvanodynamiccurvesrecordedatacelltemperatureof40 Cusingthe 850CforH 2 asreactantattheanodeandairasoxidantatthecathode:ahysteresis curveforscanrate50mA/30s;andbtheoodingregionofthehysteresiscurve. Impedanceresponserecordedfordierentcurrentdensitiesat40 Cispresented inFigure3-9.Thelow-frequencyimpedanceresponseathighercurrentdensitieshas signicantscatter;whereas,thelow-frequencyimpedanceresponseatlowercurrent densitieshascomparativelylessscatter.Theenhanceddisturbanceinthelow-frequency impedanceresponseathighercurrentdensitiesmaybeattributedtostochasticprocesses suchasooding.Thescatterinthehigh-frequencyportionoftheimpedancespectra wasunaectedbychangesincurrentdensity.Thesizeoftheintermediate-frequencyand thelow-frequencyarcsincreasedwithincreasedcurrentwhichcould,assuggestedinthe literature, 12,157 bepartiallyduetoeectofooding.Similarobservationswererecorded atothertemperatures.Figure3-10ashowsahysteresiscurveobtainedat50 C,andthe correspondingimpedanceresponseispresentedinFigure3-10b. 3.3.5TimeasaParameter Theperformanceofthefuelcellwasalsoinvestigatedwithtimeintermofpolarizationcurvesandimpedanceresponses.AspresentedinFigure3-11,theasharpdecrease inthecurrentdensitywasobservedwithtimeespeciallyapparentintheohmicandmass transportregimesofthepolarization.ImpedanceresponseispresentedinFigure3-12, overallincreaseintheimpedancewasrecordedandalsothedierentfeaturesinthe impedancespectrawereobserved. 66

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Figure3-9:Themeasurementrecordedwiththe850CforH 2 asreactantattheanodeand airasoxidantatthecathode.Theanode,thecathodeandcelltemperaturesweresetat 40 C;ahysteresiscurveforscanrate50mA/30Sec.;andbimpedanceresponsesasa functionofcurrentdensities. a b Figure3-10:Themeasurementrecordedwiththe850CforH 2 asreactantattheanode andairasoxidantatthecathode.Theanode,thecathodeandcelltemperatureswereset at50 C;ahysteresiscurveforscanrate50mA/30Sec.;andbimpedanceresponsesas afunctionofcurrentdensities. 67

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Figure3-11:Polarizationcurvegeneratedfromthesteady-statemeasurementasafunctionoftimewith850CforH 2 asreactantattheanodeandairasoxidantatcathode.The anodereactantstreamandcelltemperaturesweresetat40 0 Candthecathodereactant streamtemperatureat35 0 C.Thefuelcellwasassembledwithaserpentineowchannel, andauniformporousGDL. Figure3-12:Impedanceresponsescollectedasafunctionoftimesafunctionoftimewith 850CforH 2 asreactantattheanodeandairasoxidantatcathode.Theanodereactant streamandcelltemperaturesweresetat40 0 Candthecathodereactantstreamtemperatureat35 0 C.Thefuelcellwasassembledwithaserpentineowchannel,andauniform porousGDL. 68

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3.3.6FlowChannelasaParameter Thereactantowchanneldesignisoneoftheprominentfactorsthatinuences mass-transport.Condensedwatermayberemovedbygasow.Thus,changesinreactant owchanneldesignhavebeenproposedtoreducetheooding.Acomprehensivereviewof variousow-elddesignsdevelopedbyresearchersandcompanieshasbeenreportedinthe literature. 199 Severalauthors 149,200{205 haveinvestigatedperformanceofthefuelcellwith dierentowchannelsandhavereportedbetterperformanceincaseofaninterdigitated owchannel.Hsieh etal. 200 hasreportedbetterperformanceincaseofaninterdigitated channelascomparedwithaserpentineowpatterninthefuelcellalthoughtheyhave proposedanewowdesign.Thebetterperformanceoftheinterdigitatedowchannel wasinterrelatedasaresultofconvectiveowpromotedbytheinterdigitatedowdesign whichallowedabetterutilizationofcatalyst. 201 Thelocalconcentrationpolarizationdue tonon-uniformdistributionofreactantsinaparallelowpatternispossiblereasonof lessperformanceascomparedtoaserpentinechannelinthefuelcell. 202 Thetheoretical studyreportedbyKazim etal. 206 hasshowedthatthelimitingcurrentdensityofthe fuelcellwithaninterdigitatedoweldwasaboutthreetimesthecurrentdensitywitha conventionaloweld. Inspiteofthefactthattheinterdigitatedoweldperformsbetter,verylimited experimentalstudieshavebeenpublished.Wang etal. 4 haspresentedasystematic experimentalstudyontheperformanceofthefuelcellwithaninterdigitatedoweld byinvestigatingtheeectofcelltemperature,gashumidication,operatingpressure andreactantgasowrates.Theinterdigitatedoweldhasadvantageofconvective transportinadditionofthediusiveandcapillarytransportintheconventionalowelds thoughthepressuredropcreatedbetweennon-interconnectinginletandoutlet,promotes ooding 149 becausethepressureindownstreamislow,whichposedicultyinremoving water.Therehavebeenseveraltheoreticalstudies 73,74,150,207 publishedtoaddressthe 69

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Figure3-13:Thecongurationofthepostowchannel. problemofoodingintheinterdigitatedoweldthoughnoexperimentalstudyhasbeen reported. Theperformanceoftwoconventionalchannelsintermofpolarizationcurvesand impedancespectraispresentedinthissection.Inaddition,apostowchanneldesign, showninFigure3-14wasproposedandperformanceofthenewchannelwascompared withtheconventionalchannel.Thepolarizationcurvesobtainedfortwochannelsfrom steady-statemeasurementonthefuelcellispresentedinFigure3-14.Thelimiting currentobtainedintheinterdigitatedowchannelwasaboutdoubleofthecurrent obtainedfortheserpentineowchannel,whichconrmedtheinterdigitatedchannel betterperformer.Thisobservationwasconsistentwiththereportedliterature. 201,206 The impedanceresponseobtainedfortwochannelsinthefuelcellispresentedinFigure3-15. Theimpedancespectrahavegeneralformconsistedofonehigh-frequencycapacitive loopandoneincompletelow-frequencyinductiveloop.Theimpedanceincaseofthe interdigitatedowchannelwasfoundalotlessthantheserpentineowchannelforsame operatingconditions. Theperformanceofthepostchannelwascomparedwiththeinterdigitatedchannel forsimilarconditions.AcomparisonofpolarizationcurvesarepresentedinFigure3-16. Asseeninthisgure,theopen-circuitpotentialswerecomparableinbothchannels; however,areducedperformancewasnoticedinbothOhmicandmasstransferregimesof 70

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Figure3-14:Polarizationcurvesgeneratedfortwoowchannelsfromthesteady-state measurementwiththe850CforH 2 asreactantattheanodeandairasoxidantatthe cathode.Theanodeandcelltemperaturesweresetat40 Candthecathodetemperature at35 C.ThefuelcellwasassembledwithauniformporousGDL. Figure3-15:Impedanceresponsescollectedwiththe850Cfortwoowchannelswiththe 850CforH 2 asreactantattheanodeandairasoxidantatthecathode.Theanodeand celltemperaturesweresetat40 Candthecathodetemperatureat35 C.Thefuelcell wasassembledwithauniformporousGDL. 71

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Figure3-16:Polarizationcurvesgeneratedforthenewandaconventionalowchannels fromthesteady-statemeasurementwiththe850CforH 2 asreactantattheanodeand airasoxidantatthecathode.Theanodeandcelltemperaturesweresetat40 Candthe cathodetemperatureat35 C.ThefuelcellwasassembledwithauniformporousGDL. polarizationcurveofthenewchannel.Lowerperformanceinthesestworegimescouldbe ascribedtopoorcontactandwatermanagementissuesinthenewchannel. Theimpedanceresponseofthenewchannelwasalsocomparedaspresentedin Figure3-17bfortwochannels.Higherhigh-frequencyresponseHFRwasregistered inimpedanceresponseofthenewchannelwhichcouldbeimputedtohighercontact resistanceinthenewchannel.Impedanceresponseforcurrentdensitiesasparameterwas alsocollectedforthenewchannelwhichispresentedinFigure3-17a.Itwasobserved thatimpedanceresponseespeciallyathighcurrentdensitieshaveexhibitedmuchmore scattering.Thescatteringwasmuchpronouncedatlowfrequencyportionwhichcouldbe possibleconsequencesofwatermanagementissuesi.e.,ooding. Basedoninvestigations,itwasconcludedthatthenewchanneldesignwasworsethan theconventionalchannelintermsofperformance,thoughthedesignmaybetreatedasa pseudo-1Dchannel.Thefollowingissuescouldhavelimitedtheperformanceofthenew channel: 72

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a b Figure3-17:Impedanceresponseofthenewowchannelwith850CforH 2 asreactant attheanodeandairasoxidantatcathode.Theanodeandthecelltemperatureswere setat50 Candthecathodetemperatureat45 C.Thefuelcellwasassembledwitha uniformporousGDL;aimpedanceresponsegeneratedforthenewchannelasafunction ofcurrentdensity;andbimpedanceresponserecordedat0.4A/cm 2 forthetwochannels. 1.Contactresistance: ThehigherHFRmanifestedinimpedanceresponseofthe newchannelcouldbeascribedtopoorcontactbetweenthechannelandtheMEA. 2.Masstransportlimitation: Thelowlimitingcurrentobservedusingthepost channelmaybeattributedtopoorwatermanagement. 3.Flooding: Excessivenoisediscernedintheimpedanceresponseathighercurrent densitiescouldbeattributedtostochasticprocessessuchasooding. 73

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CHAPTER4 ERRORANALYSISOFIMPEDANCERESPONSE Themeasurement-model-basederrorstructureanalysisofimpedancedataispresentedinthischapter. 4.1Introduction Impedancespectroscopyisoftenusedtocharacterizeprocessesinfuelcells,including PEMfuelcells. 105,64,106{108 Low-frequencyinductivefeatures 144,208,209 arecommonlyseen inimpedancespectraforthefuelcellsee,forexample,Figure3reportedbyMakharia etal. 208 .Makharia etal. 208 suggestedthatsidereactionsandintermediatesinvolvedin thefuelcelloperationcanbepossiblecausesoftheinductiveloopseenatlowfrequency. However,suchlow-frequencyinductiveloopscouldalsobeattributedtonon-stationary behavior,or,duetothetimerequiredtomakemeasurementsatlowfrequencies,nonstationarybehaviorcouldinuencetheshapesofthelow-frequencyfeatures.Impedance spectratypicallyexhibitinductivefeaturesathighfrequency,andsomeauthorsreport inductiveloopsatlowfrequencies.Thehigh-frequencyinductivefeaturesareunderstood tobecausedbyinstrumentartifacts,buttheinterpretationofthelow-frequencyinductive loopsislessclear.Whilethelow-frequencyloopshavebeententativelyattributedtoside reactions, 146 theycouldalsobecausedorinuencedbynonstationaryphenomena.The objectiveofthispartoftheworkwastousethemeasurementmodelconcept 124{127 to assesstheerrorstructureoftheimpedancemeasurementstakenforthefuelcell. ArecentimpedancestudyreportedbyMakharia etal. 208 revealedacapacitiveloop atintermediatefrequenciesandaninductiveloopatlowfrequency.Thecapacitiveloop wasattributedtotheresponseofelectrochemicalreactionsoccurringinthefuelcell, andtheinductiveloopsweretentativelyattributedtosidereactionsandrelaxationof associatedreactionintermediates.Theirinterpretationisconsistentwiththatsuggested byAntoine etal. 144 whoproposedthepresenceofunspeciedreactionintermediates. Theysuggestedthatlow-frequencyinductiveloopswerearesultoftherelaxationof adsorbedspeciesinvolvedindierentstepsoftheoxygenreductionreaction.More 74

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Figure4-1:Polarizationcurvegeneratedfromthesteady-statemeasurementwith850Cfor H 2 asreactantattheanodeandairasoxidantatcathode.Theanodereactantstreamand celltemperaturesweresetat40 0 Candthecathodereactantstreamtemperatureat35 0 C. recently,Wiezell etal. 145 consideredatwo-stephydrogenoxidationreactionandreported low-frequencyinductiveloops.Theyhaveexplainedthattheinductiveloopswerethe resultofchangingdierentfactorssuchaswaterconcentration,membranethickness, hydrogenpressureandthehydrogenoxidationkinetics.Theinuenceofcarbonmonoxide poisoningonplatinumandplatinum-rutheniumanodeswasinvestigatedusingimpedance spectroscopy. 187,188 Thereportedimpedanceresponseexhibitedlowfrequencypseudoinductivebehaviorwhichwasattributedtoasurfacerelaxationprocessofcompetitive oxidationofhydrogenandcarbonmonoxideattheanode. Theinductiveloopsreportedintheliteraturearetypicallyseenatverylowfrequencies, e.g., 1mHz,atwhichsystemstationaritymustbequestioned.Theobjectiveofthis workwastousethemeasurementmodeldevelopedbyAgarwal etal. 124{127 todetermine whetherthelow-frequencyinductiveloopswereduetoorinuencedbynon-stationary behavior. ThetimerequiredtomakethemeasurementateachfrequencyisshowninFigure 4-2.Thelongtimerequiredatlowerfrequenciesmademeasurementsatthesefrequencies susceptibletobeinginuencedbynonstationarybehavior. 75

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Figure4-2:Theaveragetimerequiredforimpedancemeasurementateachfrequency. Theerrorbarsassociatedwiththestandarddeviationobtainedfromfourexperimentsis smallerthanthesymbolsusedinthegure. 4.2Results Representativeimpedancescansanderroranalysisarepresentedinthissection.The stochasticerrorstructureobtainedfromreplicatedmeasurementswasusedtoweight subsequentregressionstoassessconsistencywiththeKramers-Kronigrelations.The experimentally-determinedstochasticerrorstructurewasalsousedtoassessthequalityof theregressionsandtocalculatethecondenceintervalformodelpredictions. TheerroranalysisproceduredescribedbyAgarwal etal. 124{126 wasappliedtosets ofrepeatedimpedancespectra.Theprocedureisillustratedinthesubsequentsections forverepeatedimpedancespectra,showninFigure4-3,collectedatacurrentdensityof 0.2A/cm 2 withtheFC350. 4.2.1EvaluationofStochasticErrors FollowingtheproceduredescribedbyAgarwal etal. 125 themeasurementmodel explainedinequation2{24wasttedtoeachspectrumshowninFigure4-3usinga frequency-independentweighting.Thenumberofparameterswasconstrainedbytheneed tohavethesamenumberofparametersforeachspectrumandtherequirementthatno parameterhada 2 .4percentcondenceintervalthatincludedzero.Typically,6 Voigtelementscouldberegressedtoaspectrum.Thestandarddeviationoftheresidual 76

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Figure4-3:Fivescansofimpedancedatacollectedatacurrentdensityof0.2A/cm 2 with theFC350. errorswasusedasanestimateforthestandarddeviationofthestochasticmeasurement errors.Thesameprocedurewasappliedtoimpedancemeasurementscollectedusingthe Scribner850C.TheresultsarepresentedinFigure4-4a.Here,thecomparisonofresults oftheerroranalysisisbasedontheimpedancedatacollectedat0.2A/cm 2 forboththe 850CandtheFC350. Thelevelofstochasticerrorswasverysimilarfortheimpedancecollectedusingthe GamryFC350andtheScribner850C.Standarddeviationsnormalizedbythemodulusof theimpedancearepresentedinFigure4-4b.AsshowninFigure4-4b,thenoiselevel ofthemeasurementsvariedwithfrequencybutwasgenerallylessthan0.3percentofthe modulus. Asimilarprocedurewasappliedtodeterminethestructureofstochasticerrorsin impedancemeasurementscollectedatdierentcurrentsalongthepolarizationcurve.For agivensystem,anerrorstructuremodelcouldbedeterminedfollowingthegeneralmodel describedbyOrazem etal. 210 i.e., r = j = j Z j j + j Z r j + j Z j 2 R m + {1 77

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a b Figure4-4:ComparisonoferrorstructuresfortheFC350lledsymbolsandthe850C. The representsthestandarddeviationoftherealpartoftheimpedance,andthe 4 representstheimaginarypartoftheimpedance.Thedashedandsolidlinesrepresents theempiricalmodeloftheerrorstructuregivenbyequation4{1.astandarddeviations inunitsofimpedance;andbstandarddeviationsnormalizedbythemodulusofthe impedance. where R m isthecurrentmeasuringresistorcorrespondingtoagivencurrentrangeand ,and areconstantsdeterminedforagiveninstrumentandsetofmeasurement parameters.FortheGamryFC350,alladjustedparameterswereequaltozerowiththe exceptionof =0 : 679.FortheScribner850C,alladjustedparameterswereequaltozero withtheexceptionof =0 : 00213and =0 : 679.Linescorrespondingtoequation4{1 aregiveninFigures4-4aand4-4b.Equation4{1wasusedtoweightsubsequent regressionstoassessconsistencywiththeKramers-Kronigrelations. 4.2.2EvaluationofHigh-FrequencyBiasErrors Inprincipleacomplextofthemeasurementmodelcouldbeusedtoassessthe consistencyofimpedancedata.Sequentialregressiontoeithertherealortheimaginary partswasshowntoprovidegreatersensitivitytolackofconsistency. 126 Themeasurement modelapproachdevelopedbyAgarwal etal. 126 wasusedtoassesstheconsistencyof high-frequencydatawiththeKramers-Kronigrelations.TheVoigtmodelwasttedtothe realpartofthemeasurementwithaweightingbasedontheexperimentallydetermined stochasticerrorstructure.Theparameterssoobtainedwerethenusedtopredictthe 78

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a b Figure4-5:RegressionoftheVoigtmodeltotherealpartoftheimpedancecorresponding tothesecondofvescansgiveninFigure4-3:attotherealpartofthemeasurement; andbpredictionoftheimaginarypart.The representstheexperimentaldata,the heavysolidlinerepresentsthemeasurementmodelt,andthethinsolidlinesrepresent condenceintervals. imaginarypartofthemeasurement,andacondenceintervalforthepredictionwas calculatedbasedontheestimatedcondenceintervalsfortheregressedparameters. Datathatfelloutsideofthecondenceintervalweredeemedtobeinconsistentwiththe Kramers-Kronigrelations. ThisprocessisillustratedinFigure4-5forthesecondimpedancescanshownin Figure4-3.ThettotherealpartoftheimpedanceisgiveninFigure4-5awhere thethinsolidlinesrepresentthecondenceintervalfortheregression.Theprediction oftheimaginarypartofthemeasurementisgiveninFigure4-5b.Theprediction oftheimaginarypartoftheimpedanceisexcellentatintermediatefrequencies,buta discrepancyisseeninFigure4-5batbothhighandlowfrequencies.Regressiontothe realpartoftheimpedancegenerallyprovidesfewerparametersthandoesregressionto theimaginarypart.Forthisreason,thediscrepancyseenatlowfrequencieswasnot consideredtobesignicant. 126 Thediscrepancyathighfrequencyisseenwherethereal partoftheimpedanceapproachesasymptoticallyanitevaluecorrespondingtoasolution resistance. 79

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a b Figure4-6:NormalizedresidualerrorsfortheregressionpresentedinFigure4-5:atto therealpart,wheredashedlinesrepresentthe 2 boundforthestochasticerror;andb predictionoftheimaginarypart,wheresolidlinesrepresentthe95.4%condenceintervals forthemodelobtainedbyMonteCarlosimulations. Thediscrepancyisseenmoreclearlyintheplotsofnormalizedresidualerror,given inFigure4-6aforthettingerrorsandinFigure4-6bforthepredictionerrors. ThenormalizationbytheexperimentalvalueoftheimpedancecausesthecondenceintervallinesshowninFigure4-6btotendtoward atthepointwheretheimaginary impedancechangessign.Theanalysisshowsthattheninehighestfrequenciesfelloutside the95.4percentcondenceinterval.Thesedatawereremovedfromtheregressionset. TheconclusionthatthesepointswereinconsistentwiththeKramers-Kronigrelations issupportedbytheobservationthatthenumberofparametersthatcouldbeobtained fromacomplexregressionincreasedwhenthehigh-frequencydatawereremoved.Inother words,deletionofdatathatwerestronglyinuencedbybiaserrorsincreasedtheamount ofinformationthatcouldbeextractedfromthedata.Thebiasinthecompletedataset inducedcorrelationinthemodelparameterswhichreducedthenumberofparameters whichcouldbeidentied.Removalofthebiaseddataresultedinabetterconditioned datasetthatenablesreliableidenticationofalargersetofparameters. 126 80

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a b Figure4-7:Detailedrepresentationofimpedancedatashowingtheinconsistencyobserved athighfrequency:aexpandedviewofFigure4-5b;bexpandedviewofaNyquistrepresentationseeFigure4-3foracompletespectrum.Thelledsymbolscorrespondto datathatweredeemedinconsistentwiththeKramers-Kronigrelations. Asimilaranalysiswasperformedfortherstandsecondmeasurementsobtained byboththeFC350andthe850Cinstruments.Forallmeasurements,datameasured atfrequenciesabove1000HzwerefoundtobeinconsistentwiththeKramers-Kronig relations.Thesedatawereremovedfromthedatausedinsubsequentregressions. Itisimportanttonotethatremovalofdataforwhichtheimaginaryimpedancehad apositivevaluewasnotsucienttoeliminateinconsistencywiththeKramers-Kronig relations.AsshowninFigure4-7a,theinuenceoftheartifactextendedwellintothe domaininwhichtheimaginaryimpedancehadanegativevalue.Thelledsymbolsin Figure4-7acorrespondtodatathatweredeemedinconsistentwiththeKramers-Kronig relations.TheresultmaybeseenaswellintheNyquistplotgivenasFigure4-7b. 81

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a b Figure4-8:RegressionoftheVoigtmodeltotheimaginarypartoftheimpedancecorrespondingtotherstofvescansgiveninFigure4-3:attotheimaginarypartof themeasurement;andbpredictionoftherealpart.The representstheexperimental data,theheavysolidlinerepresentsthemeasurementmodelt,andthethinsolidlines representcondenceintervals. 4.2.3EvaluationofLow-FrequencyBiasErrors Totesttheconsistencyoftheimpedancedataatlowfrequency,theimaginarypart oftheimpedancedatawasttedusingaweightingstrategybasedontheempiricalmodel forerrorstructuregivenasequation4{1.Theparametersetsoidentiedwasusedto predicttherealpartoftheimpedance.Thecondenceintervalforthepredictionwas obtainedbyaMonteCarlosimulationbasedonthecondenceintervaloftheregressed parameters.TheprocedureisdescribedbyAwarwal etal. 126 TheVoigtmeasurementmodelwasregressedtotheimaginarypartoftheimpedance datacorrespondingtotherstscanoftheimpedancedatapresentedinFigure4-3.The results,giveninFigure4-8a,showthatthemeasurementmodelcouldprovidean excellentttotheimaginarypartofthedata,evenatthelowfrequenciesthatrevealed inductiveloops,characterizedbypositivevaluesofimaginaryimpedance.Theparameter valuesobtainedfromregressiontotheimaginarypartoftheimpedancewereusedto predicttherealpart,asshowninFigure4-8b.ThesolidlinesshowninFigure4-8b representtheupperandlowerboundsofthe95.4percent condenceintervalobtained 82

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a b Figure4-9:NormalizedresidualerrorsfortheregressionpresentedinFigure4-8:at totheimaginarypart,wheredashedlinesrepresentthe 2 boundforthestochasticerror;andbpredictionoftherealpart,wheresolidlinesrepresentthe95.4%condence intervalsforthemodelobtainedbyMonteCarlosimulations. forthemodelprediction.Thelow-frequencydatathatareoutsidethecondenceinterval canthereforebeconsideredinconsistentwiththeKramers-Kronigrelations. Amorepreciseviewoftheregressionqualityandthelevelofagreementwiththe predictedvaluescanbeseeninplotsofresidualerrors.Thenormalizedresidualerror fortheregressiontotheimaginarypartoftheimpedanceisshowninFigure4-9a wherethedashedlinesindicateupperandlowerboundsforthestochasticnoiselevel forthemeasurement.Thedashedlineswerecalculatedas 2 where wasobtained fromequation4{1.Thenormalizationbytheexperimentalvalueoftheimpedance causesthedashedlinestotendtoward atthepointwheretheimaginaryimpedance changessign.Thequalityoftheregressionisindicatedbytheobservationthatthe residualerrorsfortheregressionfallwithinthenoiseleveloftheexperiment.The normalizedresidualerrorsforthepredictedrealvalueareshowninFigure4-9b,where thesolidlinerepresentstheupperandlowerboundsofthe95.4percent condence intervalobtainedforthemodelprediction.Alackofagreementbetweenpredictedand experimentalvaluesisseenforfrequenciesbelow0.05Hz.Thedataforthefourlowest 83

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a b Figure4-10:NormalizedresidualerrorsforthetofthemeasurementmodeltothesecondscanofimpedancedatapresentedinFigure4-3:attotheimaginarypart,where dashedlinesrepresentthe 2 boundforthestochasticerror;andbpredictionofthe realpart,wheresolidlinesrepresentthe95.4%condenceintervalsforthemodelobtained byMonteCarlosimulations. frequenciesareseentofalloutsidethecondenceintervalfortheprediction.Thesepoints canbedescribedasbeinginconsistentwiththeKramers-Kronigrelations. Similarbiaserroranalyseswereperformedforsubsequentimpedancescans.Figure 4-10a,forexample,showsthenormalizedresidualerrorfortheimaginarypartofthe secondscan,andtheFigure4-10bshowsassociatedpredictederrorintherealpart ofthesecondscan.Theagreementbetweenpredictedandexperimentalvaluesisbetter forthesecondscan,showninFigure4-10b,thanfortherst,showninFigure4-9b. AlldatashowninFigure4-10bfallinsidethe95.4percentcondenceintervalfor theprediction.Thesecondandsubsequentscanswerefoundtobeconsistentwiththe Kramers-Kronigrelations. Themeasurementmodelwasalsousedtotesttheimpedancedatacollectedwith the850CforconsistencywiththeKramers-Kronigrelations.Inthiscaseaswell,some low-frequencydatawerefoundtobeinconsistentwiththeKramers-Kronigrelationsfor therstofaseriesofrepeatedmeasurements.Alldatainthesecondandsubsequent scanswerefoundtobeconsistentwiththeKramer-Kronigrelations.ThetoftheVoigt 84

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a b Figure4-11:RegressionoftheVoigtmodeltotheimaginarypartoftheimpedancefor thesecondscanoftheimpedancedatacollectedat0.2A/cm 2 withthe850C:attothe imaginarypartofthemeasurement;andbpredictionoftherealpart.The represents experimentaldata,thethicksolidlinesrepresentthemeasurementmodelt,andthethin solidlinesrepresentcondenceintervals. measurementmodeltotheimaginaryimpedancedataforthesecondscanoftheseries, forexample,isshowninFigure4-11a.Thepredictedvaluefortherealpartofthe impedanceiscomparedtoexperimentalvaluesinFigure4-11b.Thecorrespondingplots ofnormalizedresidualerroraregiveninFigures4-12aand4-12b.Thedatawere foundtobeconsistentwiththeKramers-Kronigrelationsatallfrequenciesbelow1000Hz. 4.2.4ImpedanceResponseafterErrorAnalysis AnexampleispresentedinFigure4-13oftheresultsofacomplexregressionofthe measurementmodeltoadatasetinwhichdatawereremovedthatwerefoundtobeinconsistentwiththeKramers-Kronigrelations.ThenumberofVoigtelementsobtainedby theregressionwasincreasedfrom6to8bydeletingtheinconsistentdata.Theweighting appliedfortheregressionwasbasedontheexperimentallydeterminedstochasticerror structure.ThedatawerecollectedusingtheScribner850Cat0.2A/cm 2 .Thearrowin Figure4-13showstheimpedanceestimatedfromtheslopeofthepolarizationcurveat therespectivecurrentdensity.Thezero-frequencyasymptotefortheimpedancecanbe expectedtobeequaltotheslopeofthepolarizationcurveatthatcurrentdensitysolong 85

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a b Figure4-12:ResidualerrorsfortheregressionpresentedinFigure4-11:attotheimaginarypart,wheredashedlinesrepresentthe 2 boundforthestochasticerror;andb predictionoftherealpart,wheresolidlinesrepresentthe95.4%condenceintervalsfor themodelobtainedbyMonteCarlosimulations. Figure4-13:Theresultsofcomplexregressionofthemeasurementmodeltothesecond scanoftheimpedancedatacollectedat0.2A/cm 2 withtheScribner850C.The representstheexperimentaldataandthesolidlinerepresentsthemeasurementmodelt. 86

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asthepolarizationcurveismeasuredinsuchawayastorepresentasteady-statebehavior.Kramers-Kronig-consistentlow-frequencyinductiveloopswerefoundatallcurrent densitiesforbothinstruments. 4.3Discussion Thedeterminationoferrorstructurepresentedinthisworkinvolvedtwosteps.In therst,anestimatewasobtainedfromreplicatedimpedancescansforthestandard deviationofstochasticerrorsinthemeasurement.Thiserrorstructurewasusedtoweight theregressionsemployedtocheckforconsistencywiththeKramers-Kronigrelations. Determinationofthestandarddeviationofstochasticerrorsinthemeasurementcan beusedtoguidepurchaseofinstrumentationortoguideselectionofmeasurement parameters.Fortheparametersselectedhere,thetwoimpedancesystemsprovided comparablelevelsofnoise. Thelackofconsistencyofhigh-frequencydatawiththeKramers-Kronigrelations wasobservedforallmeasurements.Theinconsistencyathighfrequenciesislikelydueto instrumentandmeasurementsystemartifacts.AsseeninFigure4-7,theinuenceofthe artifactextendedwellintothedomaininwhichtheimaginaryimpedancehadanegative value.Removalofdatawithapositiveimaginaryimpedanceisnotsucienttoeliminate theinuenceofhigh-frequencyinstrumentartifactsinimpedancemeasurements. Thelackofconsistencyoflow-frequencydatawiththeKramers-Kronigrelations,seen fortherstimpedancemeasurementinFigure4-9b,islikelyassociatedwithstart-up transients.AsdescribedinSection3.2.2,impedancemeasurementswereconductedafter repeatedcurrent-voltagecyclingtohydratethemembrane.Therstimpedancescan wasthenmeasuredafterthespeciedcurrenthadbeensetforthirtyminutesandthe correspondingpotentialwasstabilized.Theimpedanceresultsindicatethatthefuelcell hadnotreachedsteady-stateoperationdueperhapstochangestothehumidicationof themembraneand/orchangesinconsumptionofreactantsintheowchannels.The secondscanoftheimpedancedata,seeFigure4-10b,showedimprovedconsistency 87

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oflow-frequencydatawiththeKramers-Kronigrelations.Thesedatawerecollected approximatelyafter3hoursofcelloperationatthespeciedcurrent. Theestablishedstart-upprocedures, 192 includingstabilizationofpotentialataset current,werenotsucienttoensurethesteady-statecondition.Impedancespectroscopy isseentobemuchmoresensitivetotheconditionofthefuelcell.Thisworkdemonstrates theutilityofthemeasurement-modelerroranalysisforidentifyingsteady-stateoperation. Notalllow-frequencyinductiveloopswerefreeofartifactscausedbynonstationary behavior,but,onceasteady-stateoperationwasestablished,thelow-frequencyinductive loopswerefoundtobeconsistentwiththeKramers-Kronigrelations.Thelow-frequency inductiveloopsinthefuelcellcanthereforebeattributedtotheresponseofphysical processesoccurringwithinthefuelcell. 88

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CHAPTER5 INTERPRETATIONOFIMPEDANCERESPONSE Impedancemodelsweredevelopedtointerprettheimpedanceresponsepresentedin Chapter4.Themodelswereformulatedtoaccountthefundamentalprocessesofthefuel cell.Themodelresponsewerecomparedwiththeexperimentalresults.Thedetailsof ex-situmeasurementsusedtosupporttheproposedmechanismarepresentedinChapter 6. 5.1Introduction InChapter4,themeasurementmodelapproachwasusedtodemonstratethat,forthe fuelcellundersteady-stateoperation,thelow-frequencyinductiveloopswereconsistent withtheKramers-Kronigrelations.Thiswork 194 demonstratedthat,independentofthe instrumentationused,thelow-frequencyfeaturescouldbeconsistentwiththeKramersKronigrelations.Therefore,thelow-frequencyinductiveloopscouldbeattributedto processcharacteristicsandnottonon-stationaryartifacts. Theobjectiveofthisworkwastoidentifychemicalandelectrochemicalreactionsthat couldaccountforthelow-frequencyinductiveimpedanceresponseandcouldtherefore beincorporatedintomechanisticmodelsfortheimpedanceresponseofthefuelcell.The modelresponseswerecomparedtoexperimentalresults.Independentinvestigationswere alsoconductedtosupportthepossibilityoftheformationoftheintermediatesidentied inthereactionmechanisms.Thepreliminarymodeldevelopmentwasreportedinour previouswork. 211 5.2ClassofModelDevelopment Twoclassesofmodels,onewithacathodicreactionandintermediateinvolving hydrogenperoxideformation,andotherrelatedtocatalystdeactivationevokedby platinumoxideformation,wereconsideredinthework.Moredetailsaboutthereaction mechanismscanbefoundinSection2.3.Sidereactionsandintermediatesinvolvedinthe overallelectrochemicalreactionshavebeenshowntoresultinlow-frequencyinductive loops. 212 Kineticmodelsaccountingforreactionintermediateswereaddressedingreater 89

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detailinpublicationbyArmstrong etal. 213 andEpelboin etal. 212 Impedanceresponse forcoupledreactionsinvolvingintermediateunderpotentiostaticcontrolhasbeenalso illustratedelsewhere. 214 5.3ModelFramework Thedevelopmentofimpedancemodelsforspecichypothesizedreactionsequences ispresentedinthissection.Themass-transferproblemwassimpliedsignicantly byassumingthatthemembranepropertieswereuniform,thatissuesassociatedwith oodingandgas-phasetransportcouldbeneglected,andthattheheterogenousreactions tookplaceataplane, e.g., theinterfacebetweenthecatalystactivelayerandthethe protonexchangemembrane.Thispreliminaryapproachdoesnotaccountforthespatial distributionofthecatalystparticlesinthecatalystlayer,butthissimpliedtreatment issucienttoexploretheroleofspecicreactiononimpedancefeatures,suchasthe low-frequencyinductiveloops. 5.3.1PolarizationCurve Thecurrentdensitycanbeexpressedasafunctionofelectrodepotential V ,concentrationsofreactants c i atelectrodesurface,andsurfacecoverage k as i = f V;c i ; k {1 Thereactantsandproductswereassumedtodiusethroughionomeragglomeratesin thecatalystlayer.Concentrationsofreactantsandproductsatthereactionplanewere calculatedfromthebulkconcentrations c i 1 andthemass-transfer-limitedcurrent densities i lim using c i = c i 1 )]TJETq1 0 0 1 348.161 198.64 cm[]0 d 0 J 0.478 w 0 0 m 3.993 0 l SQBT/F22 11.9552 Tf 348.161 189.128 Td [(i i lim {2 where i lim = nFD i c i 1 i {3 i isthediusionlmthickness, F isFaraday'sconstant, D i isthediusivityofthe reactantthroughionomeragglomeratesinthecatalystlayer,and n isthenumberof 90

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electronexchangedinthereaction.Thesteady-statesurfacecoveragewascalculatedby materialbalanceoftheintermediatesinvolvedintheproposedreactionmechanism. Thesteady-statecurrentforeachreactionwascalculatedasfunctionofoverpotential usingthevaluesofthesteady-statesurfacecoverageandconcentrations.Thetotal steady-statecurrentwascalculatedbyaddingcurrentcontributionsfromallparticipating reactionsatthecathode,andthetotalcurrentattheanodewasequatedtothetotal currentfromthecathodetocalculatetheanodeoverpotential a i.e., a = 1 b H 2 log 0 @ i T;c K H 2 c H 2 1 1 )]TJETq1 0 0 1 370.893 525.112 cm[]0 d 0 J 0.359 w 0 0 m 2.883 0 l SQBT/F23 7.9701 Tf 370.893 518.588 Td [(i T;c i lim 1 A {4 where i T;c isthetotalcathodecurrent, K H 2 istherateconstantfortheHORdenedasin equation5{18, c H 2 istheconcentrationofthehydrogen,and b H 2 istheTafelconstantfor theHOR.Thecellpotential U wasgivenby U = U eq: )]TJ/F22 11.9552 Tf 11.955 0 Td [( c )]TJ/F15 11.9552 Tf 11.955 0 Td [( )]TJ/F22 11.9552 Tf 9.299 0 Td [( a )]TJ/F22 11.9552 Tf 11.955 0 Td [(IR e {5 where c isthecathodeoverpotentialand R e isthefrequency-independentohmicresistance. 5.3.2ImpedanceResponse TheFaradaiccurrentdensitycanbeexpressedintermsofasteadystatecontribution i andanoscillatingcontribution e i as i f = i f +Re n e i f exp j!t o {6 where j = p )]TJ/F15 11.9552 Tf 9.298 0 Td [(1, t istime,and isthefrequencyinunitsofs )]TJ/F21 7.9701 Tf 6.586 0 Td [(1 .ATaylorseries expansionofequation5{1aboutthesteady-statevalueyields e i f = @f @V c i ; k # e V + @f @c i; 0 V;c j 6 = i ; k # e c i + @f @ k V;c i ; j 6 = k # e k {7 where e V e c i and e k wereassumedtohavesmallmagnitudessuchthatthehigher-order termsintheexpansioncanbeneglected. 91

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Anexpressionfor e c i wasfoundintermsof e i f using e i f = nFD i @c i @y {8 or e c i = e i f i nFD i )]TJ/F15 11.9552 Tf 19.528 8.088 Td [(1 0 i {9 where 0 i representsthedimensionlessgradientoftheoscillatingconcentration = e c i = e c i .UndertheassumptionthatmasstransferisthroughaNernststagnantdiusion layer, )]TJ/F15 11.9552 Tf 9.298 0 Td [(1 0 i = tanh p jK i p jK i {10 where K i = 2 i D i {11 TheFaradaiccurrentwascalculatedbysummingcontributionsfromallthereactionsin accordancewiththereactionstoichiometry.Thetotalcurrentwasfoundbysummingthe interfacialchargingcurrentandtheFaradaiccurrent, i.e., i = i f + C 0 dV dt {12 where C 0 istheinterfacialcapacitance.Forasmall-amplitudesinusoidalperturbation,the totalcurrentwaswrittenas e i = e i f + j!C 0 e V {13 Ananalyticalexpressionforimpedancewascalculatedforeachmodelusing Z = e U e i = R e + e V e i {14 where U isthecellpotential,and V istheelectrodepotential. 5.4ImpedanceResponseforProposedReactionMechanisms Therelationshipbetweenthefuelcellgeometryandanequivalentcircuitdiagram forproposedreactionsequencesispresentedinFigure5-1,wheretheboxesrepresent 92

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Figure5-1:Aschematicrepresentationoftherelationshipbetweenthefuelcellgeometryandanequivalentcircuitdiagramforproposedreactionsequenceswheretheboxes representFaradaicimpedancesdeterminedforspecicreactionmechanisms. Faradaicimpedancesthataretobedeterminedforthespecicassumedreactionmechanisms.Threeimpedancemodelswereinvestigatedfortheinterpretationoflow-frequency inductiveloops.Model1incorporatesasingle-stepORRatthecathodeandasingle-step HORattheanode.Model2treatshydrogenperoxideformationinatwo-stepORRatthe cathodealongwithasingle-stepHORattheanode,andModel3includesthesingle-step ORRcoupledwiththeplatinumcatalystdissolutionatthecathodealongwithasinglestepHORattheanode.Theliteraturesuggeststhattherateshouldbeoftheorderof3/2 withrespecttoprotonconcentrationandoftheorderof1withrespecttotheoxygenconcentration. 144 Forthepresentwork,thesurfaceconcentrationoftheprotonwasassumed tobeconstantandwasthereforeincorporatedintotheeectivereactionrateconstant. 5.4.1Model1:SimpleReactionKinetics TheORR O 2 +4H + +4e )]TJ/F19 11.9552 Tf 10.406 -4.936 Td [(! 2H 2 O{15 93

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wasassumedtotakeplaceatthecathode.Thesteady-statecurrentdensityexpression correspondingtothisreactionwasassumedtobe i O 2 = )]TJ/F22 11.9552 Tf 9.299 0 Td [(K O 2 c O 2 exp )]TJ/F22 11.9552 Tf 9.299 0 Td [(b O 2 O 2 {16 where K O 2 = nFk O 2 k O 2 istherateconstant, n =4isthenumberofelectronexchanged inthereaction, b k = k F=RT k istheapparenttransfercoecientforreaction k R istheuniversalgasconstant, T isabsolutetemperature, c i istheconcentrationat electrodesurface, i = V )]TJ/F22 11.9552 Tf 10.914 0 Td [(V eq:;i i isthesurfaceoverpotential,and V eq:;i istheequilibrium potential. Thesingle-stepHOR H 2 2H + +2e )]TJ/F15 11.9552 Tf 165.004 -4.936 Td [({17 wasassumedtotakeplaceattheanode.Thecorrespondingsteady-statecurrentexpressionwas i H 2 = K H 2 c H 2 exp b H 2 H 2 {18 where K H 2 = nFk H 2 k H 2 istherateconstant,and n =2. Theoverallimpedancewascalculatedas Z = R e + 1 R t; H 2 + Z D; H 2 )]TJ/F21 7.9701 Tf 6.586 0 Td [(1 + j!C 0 ;a + 1 R t; O 2 + Z D; O 2 )]TJ/F21 7.9701 Tf 6.587 0 Td [(1 + j!C 0 ;c {19 where R e isthefrequencyindependentohmicresistance, C 0 ; c istheinterfacialcapacitance atthecathode, C 0 ; a istheinterfacialcapacitanceattheanode, R t; O 2 isthecharge-transfer resistancefortheORR, i.e., R t; O 2 = K O 2 c O 2 b O 2 exp )]TJ/F22 11.9552 Tf 9.298 0 Td [(b O 2 O 2 )]TJ/F21 7.9701 Tf 6.586 0 Td [(1 {20 Z D; O 2 isthemass-transportimpedancefortheORR, i.e., Z D; O 2 = O 2 c O 2 b O 2 4 FD O 2 )]TJ/F15 11.9552 Tf 9.299 0 Td [(1 0 O 2 {21 94

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R t; H 2 isthecharge-transferresistancefortheHOR, i.e., R t; H 2 = K H 2 c H 2 b H 2 exp b H 2 H 2 )]TJ/F21 7.9701 Tf 6.586 0 Td [(1 {22 and Z D; H 2 isthemass-transportimpedancefortheHOR, i.e., Z D; H 2 = H 2 c H 2 b H 2 2 FD H 2 )]TJ/F15 11.9552 Tf 9.298 0 Td [(1 0 H 2 {23 Theterm )]TJ/F15 11.9552 Tf 9.298 0 Td [(1 = 0 i wasgivenbyequation5{10.Equations5{20-5{23representlumped parametersthatcanbeexpressedintermsofparametersusedtodenethesteady-state polarizationcurve. TheimpedanceresponseforModel1canbeexpressedastheequivalentcircuitshown inFigure5-2afortheanodewhere R t; H 2 isgivenbyequation5{22and Z D; H 2 isgiven byequation5{23andinFigure5-2bforthecathode,where R t; O 2 isgivenbyequation 5{20and Z D; O 2 isgivenbyequation5{21. 5.4.2Model2:HydrogenPeroxideFormation TheORRwasassumedtotakeplaceintwostepsinaccordancetothereaction schemeasdiscussedintheliterature. 8 Therstreaction O 2 +2H + +2e )]TJ/F19 11.9552 Tf 10.405 -4.936 Td [(! H 2 O 2 {24 involvesformationofhydrogenperoxideH 2 O 2 whichreactsfurthertoformwater, i.e., H 2 O 2 +2H + +2e )]TJ/F19 11.9552 Tf 10.406 -4.936 Td [(! 2H 2 O{25 Crossoverofhydrogentothecathodeisreportedtofacilitatethereactionofoxygenand hydrogenatthecathode,generatinghydroxylandhydroperoxylradicalswhichreact furthertoproducehydrogenperoxideatthecathode. 100 ThehypothesisthatH 2 O 2 may beformedatthecathodeoffuelcellissupportedbytheresultsofInaba etal. 77 They reportedthatformationofperoxidebyatwo-electronpathwasfavoredoverformation ofwaterbyafour-electronpathinORRonnanoparticlesofPtsupportedoncarbonat 95

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a b c d Figure5-2:Equivalentcircuitdiagramsforproposedreactionsequenceswheretheboxes representdiusionimpedancesorFaradaicimpedancesdeterminedforspecicreaction mechanisms:aanodeforallmodels;bcathodeforModel1;ccathodeforModel2;and dcathodeforModel3. 96

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cathodicpotential.Whiletheirworksupportsformationofperoxideatthecathodeof thefuelcell,peroxideformationattheanodeisalsopossibleduetoO 2 crossover.Amore inclusiveimpedancemodelcouldbedevelopedbyaccountingforperoxideformationatthe anode. Thesteady-statecurrentforreaction5{24canbeexpressedas i O 2 = )]TJ/F22 11.9552 Tf 9.299 0 Td [(K O 2 c O 2 )]TJ/F22 11.9552 Tf 11.956 0 Td [( H 2 O 2 exp )]TJ/F22 11.9552 Tf 9.299 0 Td [(b O 2 O 2 {26 where K O 2 = nFk O 2 withthesamenotationdenedforModel1, n =2,and H 2 O 2 isthe fractionalsurfacecoverageofhydrogenperoxide.Thecurrentdensitycorrespondingtothe reaction5{25canbeexpressedas i H 2 O 2 = )]TJ/F22 11.9552 Tf 9.299 0 Td [(K H 2 O 2 H 2 O 2 exp )]TJ/F22 11.9552 Tf 9.299 0 Td [(b H 2 O 2 H 2 O 2 {27 where K H 2 O 2 = nF )]TJ/F22 11.9552 Tf 7.314 0 Td [(k H 2 O 2 n =2,and)-326(isthemaximumsurfacecoverage.The electrochemicalreactionattheanodewasgivenasreaction5{17,andthecorresponding currentexpressionwasgivenasequation5{18.Diusionofperoxideawayfromthe catalystsurfacewasignoredinthepresentwork.Thus,theperoxideproducedbyreaction 5{24wassubsequentlyconsumedinreaction5{25toformwater. Theoverallimpedancewascalculatedas Z = R e + 1 1 R t; H 2 + Z D; H 2 + j!C 0 ;a + 1 Z e + A j 2)]TJ/F23 7.9701 Tf 9.522 0 Td [(F! )]TJ/F23 7.9701 Tf 6.587 0 Td [(B + j!C 0 ;c {28 where Z e = 1 R t; O 2 + Z D; O 2 + 1 R t; H 2 O 2 {29 A = 1 R t; O 2 + Z D; O 2 )]TJETq1 0 0 1 226.405 167.068 cm[]0 d 0 J 0.478 w 0 0 m 6.722 0 l SQBT/F22 11.9552 Tf 226.405 160.247 Td [( H 2 O 2 )]TJ/F15 11.9552 Tf 42.475 8.088 Td [(1 R t; H 2 O 2 H 2 O 2 1 R t; O 2 + Z D; O 2 )]TJ/F15 11.9552 Tf 28.249 8.088 Td [(1 R t; H 2 O 2 {30 and B = 1 R t; O 2 + Z D; O 2 )]TJETq1 0 0 1 312.43 112.777 cm[]0 d 0 J 0.478 w 0 0 m 6.722 0 l SQBT/F22 11.9552 Tf 312.43 105.956 Td [( H 2 O 2 )]TJ/F15 11.9552 Tf 42.476 8.088 Td [(1 R t; H 2 O 2 H 2 O 2 {31 97

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Inequation5{29, R t; O 2 isthecharge-transferresistancefortherststepoftheORR, i.e., R t; O 2 = K O 2 c O 2 b O 2 )]TJETq1 0 0 1 314.975 667.05 cm[]0 d 0 J 0.478 w 0 0 m 6.722 0 l SQBT/F22 11.9552 Tf 314.975 660.229 Td [( H 2 O 2 exp )]TJ/F22 11.9552 Tf 9.299 0 Td [(b O 2 O 2 )]TJ/F21 7.9701 Tf 6.586 0 Td [(1 {32 Z D; O 2 isthemass-transferimpedancefortherststepoftheORR, i.e., Z D; O 2 = O 2 c O 2 b O 2 2 FD O 2 )]TJ/F15 11.9552 Tf 9.299 0 Td [(1 0 O 2 {33 and R t; H 2 O 2 isthecharge-transferresistanceforthesecondstepoftheORR, i.e., R t; H 2 O 2 = K H 2 O 2 b H 2 O 2 H 2 O 2 exp )]TJ/F22 11.9552 Tf 9.298 0 Td [(b H 2 O 2 H 2 O 2 )]TJ/F21 7.9701 Tf 6.587 0 Td [(1 {34 Thesteady-statesurfacecoverageoftheperoxideisgivenas: H 2 O 2 = K O 2 c O 2 b O 2 exp )]TJ/F22 11.9552 Tf 9.299 0 Td [(b O 2 O 2 K O 2 c O 2 b O 2 exp )]TJ/F22 11.9552 Tf 9.298 0 Td [(b O 2 O 2 + K H 2 O 2 b H 2 O 2 exp )]TJ/F22 11.9552 Tf 9.299 0 Td [(b H 2 O 2 H 2 O 2 {35 Expressionsfor R t; H 2 and Z D; H 2 weregivenbyequations5{22and5{23,respectively, asdenedinModel1. TheimpedanceresponseforModel2canbeexpressedastheequivalentcircuitshown inFigure5-2afortheanodeandFigure5-2cforthecathode.TheboxesinFigures 5-2arepresentadiusionimpedancecorrespondingtotransportofhydrogen,andthe boxesinFigure5-2crepresenttheFaradaicimpedancescorrespondingtotheproposed reactionsequence.Theterm Z c inFigure5-1isgivenby Z c = 1 Z O 2 + 1 Z H 2 O 2 )]TJ/F21 7.9701 Tf 6.587 0 Td [(1 {36 Itshouldbeemphasizedthat Z O 2 isnotthesumof R t; O 2 and Z D; O 2 duetothesurface coverage.Similarly, Z H 2 O 2 cannotbeconsideredtobeafrequency-independent R t; H 2 O 2 98

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5.4.3Model3:PlatinumDissolution Theplatinumdissolutionwasassumedtooccurbyareactionschemesimilartothat reportedbyDarling etal., 10 i.e., byanelectrochemicalreaction Pt+H 2 O PtO+2H + +2e )]TJ/F15 11.9552 Tf 128.964 -4.937 Td [({37 inwhichPtOisformed,followedbyachemicaldissolutionreaction PtO+2H + Pt +2 +H 2 O{38 ThemodeldevelopedbyDarlingandMeyersresultedinanequilibriumoxidecoverage byPtO. 10 AsimilarreactionschemeforPtdissolutionwithPtOasanintermediateat thecathodicpotentialofthefuelcellhasalsobeenreportedbyDam etal. 91 Also,Xu et al. 215 havereportedtwoschemesforPtoxidationatthecathode,bothhavingPtOasan intermediate. Thecurrentdensitycorrespondingtoreaction5{37wasgivenby i Pt = K Pt ;f )]TJ/F22 11.9552 Tf 11.955 0 Td [( PtO exp b Pt ;f Pt ;f )]TJ/F22 11.9552 Tf 11.956 0 Td [(K Pt ;b PtO exp )]TJ/F22 11.9552 Tf 9.299 0 Td [(b Pt ;b Pt ;b {39 where K Pt ;f = nF )]TJ/F22 11.9552 Tf 7.314 0 Td [(k Pt ;f K Pt ;b = nFk Pt ;b n =2,)-327(isthemaximumsurfacecoverage,and PtO isthefractionalsurfacecoveragebyPtO.ThedissolutionofPtOwasassumedto occuraccordingto r PtO = K 3 PtO {40 andthecorrespondingmaterialbalanceforthePtOwasexpressedas )]TJ/F22 11.9552 Tf 8.51 8.088 Td [(@ PtO @t = i Pt 2 F )]TJ/F22 11.9552 Tf 11.956 0 Td [(r PtO {41 Theformationoftheplatinumoxidewasproposedtohaveanindirectinuenceon theORRatthecathodebychangingtheeectiverateconstantforthereaction.Thus, K e = K Pt + K PtO )]TJ/F22 11.9552 Tf 11.955 0 Td [(K Pt PtO {42 99

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where K Pt istherateconstantonaplatinumsiteand K PtO istherateconstantona platinumoxidesite.TheORRwasassumedtotakeplaceaccordingtoreaction5{15 withasteady-statecurrentdensitygivenby i O 2 = )]TJ/F22 11.9552 Tf 9.299 0 Td [(K e c O 2 exp )]TJ/F22 11.9552 Tf 9.299 0 Td [(b O 2 O 2 {43 where K e isdenedbyequation5{42. Theoverallimpedancewascalculatedtobe Z = R e + 1 1 R t; H 2 + Z D; H 2 + j!C 0 ;a + 1 Z e + A 2 F j )]TJ/F23 7.9701 Tf 5.289 0 Td [(! + K 3 + B + j!C 0 ;c {44 where Z e = 1 R t; O 2 + Z D; O 2 + 1 R Pt ;f + 1 R Pt ;b {45 A = K PtO )]TJ/F22 11.9552 Tf 11.956 0 Td [(K Pt K e b O 2 )]TJ/F15 11.9552 Tf 60.231 8.087 Td [(1 R Pt ;f b Pt ;f )]TJETq1 0 0 1 280.491 430.057 cm[]0 d 0 J 0.478 w 0 0 m 6.722 0 l SQBT/F22 11.9552 Tf 280.491 423.236 Td [( PtO )]TJ/F15 11.9552 Tf 44.123 8.087 Td [(1 R Pt ;b b Pt ;b PtO 1 R Pt ;f + 1 R Pt ;b {46 and B = 1 R Pt ;f b Pt ;f )]TJETq1 0 0 1 298.538 375.766 cm[]0 d 0 J 0.478 w 0 0 m 6.722 0 l SQBT/F22 11.9552 Tf 298.538 368.944 Td [( PtO + 1 R Pt ;b b Pt ;b PtO {47 Inequation5{45, R t; O 2 isthecharge-transferresistancefortheORR, i.e., R t; O 2 = K e c O 2 b O 2 exp )]TJ/F22 11.9552 Tf 9.298 0 Td [(b O 2 O 2 )]TJ/F21 7.9701 Tf 6.586 0 Td [(1 {48 Z D; O 2 isthemass-transportimpedancefortheORR, i.e., Z D; O 2 = O 2 c O 2 b O 2 4 FD O 2 )]TJ/F15 11.9552 Tf 9.299 0 Td [(1 0 O 2 {49 R Pt ;f isthecharge-transferresistancefortheforwardreaction, i.e., R Pt ;f = K Pt ;f b Pt ;f )]TJETq1 0 0 1 306.907 174.268 cm[]0 d 0 J 0.478 w 0 0 m 6.722 0 l SQBT/F22 11.9552 Tf 306.907 167.447 Td [( PtO exp b Pt ;f Pt ;f )]TJ/F21 7.9701 Tf 6.586 0 Td [(1 {50 and R Pt ;b isthecharge-transferresistanceforthebackwardreaction, i.e., R Pt ;b = K Pt ;b b Pt ;b PtO exp )]TJ/F22 11.9552 Tf 9.299 0 Td [(b Pt ;b Pt ;b )]TJ/F21 7.9701 Tf 6.586 0 Td [(1 {51 100

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Thesteady-statesurfacecoverageoftheplatinumoxideisgivenas PtO = K Pt ;f b Pt ;f exp b Pt ;f Pt ;f K Pt ;b b Pt ;f exp b Pt ;f Pt ;f + K Pt ;b b Pt ;b exp )]TJ/F22 11.9552 Tf 9.299 0 Td [(b Pt ;b Pt ;b +2 FK 3 {52 Model3wasderivedforageneralexpressionof K e asdescribedinequation5{42but for K PtO <
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a b Figure5-3:ElectrochemicalresultsobtainedwithH 2 asreactantattheanodeandair asoxidantatthecathode.Theanodeandcelltemperatureswere40 C,andthecathode temperaturewas35 C.aPolarizationcurve;andbimpedanceresponsewithcurrent densityasaparameter. 5.5.1ExperimentalPolarizationandImpedanceResults ThepolarizationcurveforthefuelcellispresentedinFigure5-3a.Thecellresponse isstronglyinuencedbyreactionkineticsatlowcurrentdensities.Theinuenceofthe Ohmicpotentialdropisevidentatintermediatecurrentdensities,andthemass-transfer limitationsareevidentatlargecurrentdensities. Toexplorethebehaviorofthefuelcell,theimpedancewasmeasuredatseveral pointsonthepolarizationcurve.TypicalimpedancespectraarepresentedinFigure 5-3bforcurrentdensitieschosentoberepresentativeofthekinetic,ohmic,andmasstransfercontrolledregionsofthepolarizationcurve.Theimpedancespectrahavea generalformconsistingofonehigh-frequencycapacitiveloopandoneincompletelowfrequencyinductiveloop.SimilarinductiveloopswerereportedbyMakharia etal. 208 forsmallcurrentdensitiesinwhichkineticlimitationsdominate.Thepresentwork demonstratesthatsimilarlow-frequencyinductiveloopscanbeobservedforallregionsof thepolarizationcurve. 5.5.2ModelResponseAnalysis Equations5{19,5{28,and 5{44 providemathematicalexpressionsforthe impedanceresponseofafuelcellassociatedwiththereactionmechanismsdescribedin 102

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Table5-1:ParametersusedtocalculatetheimpedanceresponsecorrespondingtoModels 1,2,and3. Parameters Model1 Model2 Model3 D O 2 ; m 2 = s 4 10 )]TJ/F21 7.9701 Tf 6.586 0 Td [(11 4 10 )]TJ/F21 7.9701 Tf 6.586 0 Td [(11 4 10 )]TJ/F21 7.9701 Tf 6.586 0 Td [(11 D H 2 ; m 2 = s 4 10 )]TJ/F21 7.9701 Tf 6.587 0 Td [(9 4 10 )]TJ/F21 7.9701 Tf 6.586 0 Td [(9 4 10 )]TJ/F21 7.9701 Tf 6.586 0 Td [(9 D H 2 O 2 ; m 2 = s 4 10 )]TJ/F21 7.9701 Tf 6.586 0 Td [(15 ; m 1 10 )]TJ/F21 7.9701 Tf 6.587 0 Td [(6 1 10 )]TJ/F21 7.9701 Tf 6.586 0 Td [(6 1 10 )]TJ/F21 7.9701 Tf 6.586 0 Td [(6 R e ; cm 2 0.135 0.135 0.135 C 0 ;F 0.212 0.212 0.212 b H 2 ;V )]TJ/F21 7.9701 Tf 6.587 0 Td [(1 65 40 40 b O2 ;V )]TJ/F21 7.9701 Tf 6.586 0 Td [(1 27 27 45 b H 2 O 2 ;V )]TJ/F21 7.9701 Tf 6.586 0 Td [(1 15 b Pt ;V )]TJ/F21 7.9701 Tf 6.587 0 Td [(1 14 K H 2 ; Acm = mol 0.55 1.34 1.35 K O 2 ; Acm = mol 961.9 10900 10900 K H 2 O 2 ; A = mol 1900 K Pt ; Acm = mol 6.2 K PtO ; Acm = mol 0.01 K 3 ; mol = s 0.01 K Pt ; f ; A = mol 0.01 K Pt ; b ; A = cm 2 0.01 theprevioussections.Thesemodelswerecomparedtotheexperimentalpolarization andimpedancedata.Themethodemployedwastocalculatethepolarizationcurvethat matchedcloselytheexperimentalresultsandthentousethesameparameterstoestimate theimpedanceresponseatdierentcurrents.Directregressionwasnotemployedasthe modeldoesnotaccountexplicitlyforthenon-uniformreactionratesalongthelengthof theserpentineowchannels. ModelparametersarepresentedinTable5-1.Constantvalueswereassumedforthe interfacialcapacitance,ionicresistanceinthecatalystlayer,membraneresistance,and oxygenpermeabilitythroughionomeragglomeratesinthecatalystlayer.Whenappropriate,numericalvaluesweretakenfromtheliterature. 64 Theimpedanceresponseforall simulationscorrespondedtoafrequencyrangeof10kHzto0.001mHz.Calculationsat lowfrequencywereusedtoexploremorefullythelow-frequencyinductivefeatures. 103

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Figure5-4:PolarizationcurvegeneratedbyModel1for40 Cusingparametersreported inTable5-1andcomparedwiththeexperimentaldatapresentedinFigure5-3a. 5.5.2.1Model1 ThepolarizationcurvegeneratedfromModel1iscomparedtoexperimentaldatain Figure5-4.Theparametersusedtogeneratethepolarizationcurvewerethenusedto calculatetheimpedanceresponse.Theresultsforanintermediate-current.2A/cm 2 are comparedinFigure5-5totheexperimentaldata.TheimpedanceresponseforModel1 consistedofonecompressedcapacitiveloopwithastraight-lineportionathighfrequency. Similarimpedancespectrahavebeenreportedintheliterature. 107,65,216 Thecapacitive arccanbeattributedtothesingle-stepORRatthecathode.Thestraight-lineportion atthehigherfrequenciescanbeattributedtomasstransportimpedanceassociatedwith diusionofoxygen.Model1providesareasonablerepresentationofthecapacitiveloops, butcannotaccountfortheinductiveloopsseenatlowfrequency. TheinabilityofModel1toaccountforthelow-frequencyinductiveloopsisseenmore clearlyinFigures5-6aand5-6b,wheretherealandimaginarypartsoftheimpedance arepresented,respectively,asfunctionsoffrequency.Model1providedsimilaragreement totheexperimentalresultsatbothlowerandhighercurrentdensities.Thus,themodel 104

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Figure5-5:Impedanceresponsefor0.2A/cm 2 generatedbyModel1for40 CusingparametersreportedinTable5-1andcomparedwiththeexperimentaldatapresentedin Figure5-3b. a b Figure5-6:Impedanceresponsefor0.2A/cm 2 generatedbyModel1for40 CusingparametersreportedinTable5-1;arealpartoftheimpedanceofthemodelresponsecomparedwiththeexperimentaldatapresentedintheFigure5-3b;andbimaginarypartof theimpedanceofthemodelresponsecomparedwiththeexperimentaldatapresentedin Figure5-3b. 105

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Figure5-7:PolarizationcurvegeneratedbyModels2and3for40 CusingparametersreportedinTable5-1andcomparedwiththeexperimentaldatapresentedinFigure5-3a. thataccountsforonlythehydrogenoxidationandoxygenreductionreactionscannot explaintheinductivebehavioratlowfrequencies. 5.5.2.2Models2and3 ThepolarizationcurvesgeneratedwithModels2and3arepresentedinFigure5-7. Thepresenceofthesidereactionsinthemodelhaslittlediscernableinuenceonthe polarizationcurvebecausethesereactionsareassumedtobetakingplaceatalowrate ascomparedtothedominanthydrogenoxidationandoxygenreductionreactions.The relativecontributionsofthedierentreactionsatthecathodeareshowninFigure5-8. AsshowninFigure5-8a,thetworeductionstepsinModel2contributedequallytothe totalcurrentbecausethedesorption/lossofperoxidewasnotconsideredinthemodel development.ThecontributiontototalcurrentbyplatinumdissolutionshowninFigure 5-8bwasfoundtobenegligibleascomparedtooxygenreduction. TheimpedanceresponseforthemodelwiththehydrogenperoxideformationModel 2consistedofonehigh-frequencycapacitiveloopandonelow-frequencyinductiveloop. TheimpedanceresponseforthemodelaccountingforplatinumdissolutionModel3 alsoconsistedofonehigh-frequencycapacitiveloopandonelow-frequencyinductive 106

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a b Figure5-8:Relativecontributionsoftworeactionstototalcurrentatthecathode:a Model2;andbModel3. Figure5-9:Impedanceresponsefor0.05A/cm 2 generatedbyModels2and3for40 CusingparametersreportedinTable5-1andcomparedwiththeexperimentaldatapresented inFigure5-3b. loop.AcomparisonbetweenthemodelandexperimentispresentedinNyquist-format inFigure5-9forcurrentdensitiesinthekineticallycontrolledpartofthepolarization curve.Therealandimaginarypartsoftheimpedancearepresentedasfunctionsof frequencyinFigures5-10aand5-10b,respectively.Similarresultsareshownin Figures5-11,5-12a,and5-12bfortheintermediatecurrentdensityandinFigures 5-13,5-14a,and5-14bforhighcurrentdensities.Impedancemeasurementsaremuch moresensitivethanpolarizationcurvestothepresenceofminorreactions.BothModels2 107

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a b Figure5-10:Impedanceresponsefor0.05A/cm 2 generatedbyModels2and3for40 CusingparametersreportedinTable5-1:arealpartoftheimpedanceofthemodel responsecomparedwiththeexperimentaldatapresentedinFigure5-3b;andbimaginarypartoftheimpedanceofthemodelresponsecomparedwiththeexperimentaldata presentedinFigure5-3b. Figure5-11:Impedanceresponsefor0.2A/cm 2 generatedbyModels2and3for40 CusingparametersreportedinTable5-1andcomparedwiththeexperimentaldatapresented inFigure5-3b. 108

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a b Figure5-12:Impedanceresponsefor0.2A/cm 2 generatedbyModels2and3for40 CusingparametersreportedinTable5-1:arealpartoftheimpedanceofthemodelresponse comparedwiththeexperimentaldatapresentedinFigure5-3b;andbimaginarypartof theimpedanceofthemodelresponsecomparedwiththeexperimentaldatapresentedin Figure5-3b. Figure5-13:Impedanceresponsefor0.3A/cm 2 generatedbyModels2and3for40 CusingparametersreportedinTable5-1andcomparedwiththeexperimentaldatapresented inFigure5-3b. 109

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a b Figure5-14:Impedanceresponsefor0.3A/cm 2 generatedbyModels2and3for40 CusingparametersreportedinTable5-1:arealpartoftheimpedanceofthemodelresponse comparedwiththeexperimentaldatapresentedinFigure5-3b;andbimaginarypartof theimpedanceofthemodelresponsecomparedwiththeexperimentaldatapresentedin Figure5-3b. and3werefoundtobecapableofyieldinglow-frequencyinductiveloopsatallportionsof thepolarizationcurve. 5.6Discussion Theinductiveloopsseeninlow-frequencyimpedancemeasurementsforthefuelcell havegainedrecentattentionintheliterature.Severalexplanationshavebeenproposed. Modelsforimpedanceresponsearenotunique,andmanymodelscanleadtospecic featuressuchasthelow-frequencyinductiveloopsdescribedinthepresentwork.The inuenceofcarbonmonoxidepoisoningontheanodekineticshasbeeninvokedbyseveral authors. 106,119,187,122 Thecathodekineticswerelimitinginthecongurationemployed inthepresentexperiments,whichusedasymmetricplatinumloading.Inaddition,the anodeandcathodegasesusedwereratedultra-pure,sotheinuenceofcarbonmonoxide couldbeexcludedforthepresentexperiments.Wiezell etal. 145,217 haveproposedthat non-uniformwatertransportintheanodecouldleadtolow-frequencyinductiveloopsdue totheinuenceofwaterontheanodekinetics.Suchanexplanationdoesnotapplyfor thepresentexperimentsastheyweredominatedbycathodekinetics. 110

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a b Figure5-15:Fractionalsurface-coverageoftheintermediatesplottedaasafunctionof cellpotential;andbasafunctionofcurrentdensity. Severalauthorshaveproposedthatthelow-frequencyinductiveloopscouldbe attributedtorelaxationofadsorbedintermediatesspeciesassociatedwithcathodic reactions. 208,144,209 Thepresentworkshowsthatcathodicreactionsinvolvingformation ofperoxideintermediatesandreactionsinvolvingformationofPtOandsubsequent dissolutionofplatinumcanresultinlow-frequencyinductiveloops.Aninterestingaspect ofModel3isthattheinductiveloopiscontrolledbyformationofPtO.Thecorresponding low-frequencyinductiveloopscanbeseenevenatverylowratesofPtdissolution.These interpretationsaresupportedbyagrowingnumberofarticlesintherecentliterature describingevidenceofperoxideformationandplatinumdissolutionundernormalPEM operatingconditions. 87,96{98,93,90,99 Modelsbasedonproposedreactionhypothesiscanbeusedtogaininsightintothe reactionmechanism.Forexample,Models2and3,respectively,invokedsurfacecoverage byperoxideandPtO.Thesurfacecoveragepredictedbythesemodelsispresentedin Figures5-15aand5-15basfunctionofpotentialandcurrentdensity,respectively.As showninFigure5-15a,thefractionalcoverageoftheintermediatesinboththemodels increasedwiththeincreaseinthecellpotential.ThepresentationinFigure5-15bas 111

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afunctionofcurrentdensityshowsthatthefractionalcoverageoftheintermediates decreaseswithincreasingcurrent. Themodelspresentedinthepresentwork,whilebasedonplausiblereactionmechanisms,areambiguous.Boththereactionsinvolvingadsorbedperoxideandformation ofPtOwerecapableofpredictingthelow-frequencyinductiveloopsobservedinthe impedanceresponseofthefuelcell.Thisworkdemonstratestheneedtocouplethe impedancemeasurementswithsupportingexperimentstoidentifythereactionstaking placewithinthesystem. 218 Experimentalresultscanbefoundintheliteraturethat supportbothreactionmechanisms. 112

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CHAPTER6 RESULTSOFEX-SITUANALYSIS TheevidenceoftheintermediatesproposedforthemodeldevelopmentinChapter5 ispresentedinthischapter. 6.1Introduction PEMfuelcellsareelectrochemicalreactorsthatconvertchemicalenergyintoelectricalenergy.Thesearepromisingenergyconvertersinthe21 th centurybecauseoftheir pollutionfreecharacteristicandhighpowerdensity;however,severalissuesunresolved whichhavelimitedcommercializationofthistechnologyonalargescale.Durabilityand lowperformanceisoneoftheissueswhichcouldarisefromseveralfactorssuchasside reactionsandintermediatesinvlovingperoxideformation, 7{9 catalystdeactivationevoked byplatinumoxidationanddissolution, 10 catalystsupportlossduetocarboncorrosion, 11 watermanagementissuesincludingooding,anddrying 12 etc. InChapter5,analyticimpedancemodelswerederivedfromconsiderationofspecic reactionsequencesproposedtotakeplaceinthefuelcell. 219 Twoclassofmodels,onewith side-reactionandintermediateinvolvinghydrogenperoxideformation,andotherrelated tocatalystdeactivationevokedbyplatinumoxideformation,wereconsideredinthework. Boththemodelswerecapableofpredictingthelow-frequencyinductiveloopsobservedin theimpedanceresponseofthefuelcell.Themodelspresentedinthework,whilebasedon plausiblereactionmechanisms,areambiguous.Theworkdemonstratedtheneedtocouple theimpedancemeasurementswithsupportingexperimentstoidentifythereactionstaking placewithinthesystem. Theobjectofthisworkwastoperformexperimentswhichmayprovideanevidence oftheproposedreactionmechanisms.ThesurfacecharacteristicandmorphologicaldetailsofcatalystparticlesoftheMEAwasstudiedwiththescanningelectronmicroscope SEM. 101,31 TheTEMwasusedforatomic-scalemicro-structuralandchemicalcharacterizationoftheMEA. 100,94,33 XPSX-rayPhotoelectronSpectroscopywasutilizedto studyoxidationstateofmetalsplatinumincatalystlayer.TheXPSwasusedtoinspect 113

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possibleelementsandcompoundsatthesurface-15atomiclayersoftheMEA.The performanceofthefuelcellwasalsoinvestigatedwithtimeinformofpolarizationcurves andimpedanceresponses.ICP-MSInductivelyCoupledPlasma-MassSpectroscopywas appliedtoestimateplatinumconcentration 94 ineuentwaterofthefuelcell. 6.2Experimental Theexperimentalsystemandtheimpedanceinstrumentationusedarepresentedin thissection. 6.2.1MaterialsandChemicals ThemembraneelectrodeassemblyMEApurchasedfromIonPower,Inc.,New Castle,DEemployed0.0508mmmilsthickNaonN112withcatalystlayersof about0.025mmonbothsidesofthemembrane.Theactivesurfaceareawas5cm 2 ThecatalystlayerswereplatinumsupportedoncarbonwithaPtcatalystloadingof0.4 mg/cm 2 onboththeanodeandthecathodesides.ThegasdiusionlayerGDLused hasananeectivethicknessof0.284mm,andwasmadeofcarbonclothwithuniform macro-pores.Theowchannelusedwasserpentineinconguration.Thematerialof theowchannelwasgraphitewiththeoutletlowerthantheinlettofacilitateremoval ofcondensedwater.Atorqueof45inch-poundswasappliedtothefuelcellassembly. Hydrogengaswasusedasfuelanda79%N 2 and21%O 2 mixturewasusedasoxidant. CompressedN 2 wasusedtopurgethefuelcellbeforeandafterexperiments.ABarnstead E-PureWaterSystemwithanionresistivityof14.9Mcmwasusedasasourceof deionizedwaterdeliveredtotheanodeandthecathodehumidiers. An850Cfuel-cellteststationsuppliedbyScribnerAssociates,SouthernPines,NC wasusedtocontrolreactantowratesandtemperatures.Theteststationwasconnected toacomputerbyaninterfacefordataacquisition.Thegasowswerehumidiedto100 percentrelativehumidityattherespectivetemperatures.Thehydrogenowratewas 0.1liters/min,andtheairowratewas0.5liters/min.Themaximumstoichiometry 114

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forhydrogenandairwas1.5and2.5,respectively,andthecellwasoperatedatthe fully-humidiedcondition. 6.2.2ElectrochemicalImpedanceMeasurements Impedancemeasurementswereperformedwiththe850Cfuel-cellteststation,which containsanelectronicloadandimpedancemeasurementcapability.Allelectrochemical measurementswereperformedwithatwo-electrodecell.Theanodewasusedasapseudoreferenceelectrode.Theimpedancemeasurementswereconductedingalvanostatic modeforafrequencyrangeof10kHzto5mHzwitha10mApeak-to-peaksinusoidal perturbation.Thecorrespondingpotentialperturbationrangedfrom0.04mVto0.4mV. Theperturbationamplitudeselectedwasthelargestamplitudethatdidnotcausevisible distortionsinlow-frequencyLissajousplots.Thefrequencieswerespacedinlogarithmic progressionwith10pointsperfrequencydecade.Impedancescanswereconductedin auto-integrationmodewithaminimumof2cyclesperfrequencymeasured. 6.2.3AgingProtocolfortheSamples Thefreshsamplewasanalyzedasreceivedfromthevendor.Theagedsamplewas usedinthefuelcellforaperiodof3monthsoperatingatvarioussteadycurrentloadsfor 9hours/dayofatotalperiodof600hours. 6.2.4SurfaceAnalysis Severalmicrostructuralcharacterizationstechniqueswereemployedtostudythe morphology,sintering,andoxidationstateofelementsinthecathodecatalystlayerofthe MEA. 6.2.4.1Scanningelectronmicroscope Forsamplepreparation,asmallportionfromthecenterofthebothfreshandused MEAwascutwithsharprazorandtheSEMimagesweretakenwiththeJOELJSM6400 availableatMAICintheUniversityofFlorida. 115

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6.2.4.2Transmissionelectronmicroscope TheTEMstudywasperformedwithaJOELJSM-2010FFieldEmissionElectron MicroscopeavailableatMAICintheUniversityofFlorida,whichisequippedwithan energydispersivespectrometerEDSforcompositionalanalysis.TheTEMmicrographs weretakenat200kVacceleratingvoltageforseveralmagnicationsinbrighteld modetransmittedelectrons.Sampleswerepreparedfollowingprocedurereported inliterature. 193 AsmallportionfromthecenterofthebothfreshandusedMEAwas cutwithsharprazorandwasembeddedonepoxyresinAraldite5002for48hoursat 60 C.Thinnmsectionsfromthemembrane-electrodesinterfaceswerecutwitha diamondknifeonReichertOMU3ultramicrotomeatroomtemperature.Thesampleswere mountedonCugridmeshsize200priortoTEMstudy. 6.2.4.3X-rayphotoelectronspectroscopy TheXPSwasusedtoinspectpossibleelementsandcompoundsatthesurface -15atomiclayersoftheMEA.Forsamplepreparation,asmallportionfromthe centerofthebothfreshandusedMEAwascutwithsharprazorandtheXPSscans weretakenwiththePHI5100ESCAsystembyPerkin-ElmeravailableatMAICinthe UniversityofFlorida.X-raysourcewasMganodewithaworkfunction4.8eV.The emittedelectronswerecollectedat45 0 withrespecttothesample.Thesamplewas scannedat300wattspowerinenergyrangeof1000-0eVbindingenergywithastepof 0.5eVand30mSec/step.Thesurveyfullscanwasgeneratedatpassenergy89.45eV whereasnarrowscanshighresolutionforseveralpeakswereperformedatpassenergy of22.36eV.Theatomswereassignedaccordingtobindingenergyofvisiblepeaksand atomiccompositionofelementswereevaluatedbyrelativesintensitiesofthepeaks. 6.3Results Theresultsobtainedfromthesurfaceanalysisofthecathodesurface,andsupporting observationobtainedfromelectrochemicalresponse,andeuentanalysisarepresentedin thissection. 116

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6.3.1MicrostructuralCharacterization Thefull-scanXPSspectraispresentedinFigure6-1.Itwasdiscernedthatthepeak intensitiesofF,CwasreducedintheusedsamplewhereastheintensitiesofPtandO wereenhanced.Theamountofcarboncoulddecreaseduetocorrosionandenhanced amountofoxygencanbeascribedtosurfaceoxidationofPtinelectrodes.Anincrease intheelementalcompositionofPtandOwasnoticedintheusedMEA,whichcould supporttheformationofPtOintheusedMEA.ApeakofPtOwasdetectedinthe spectraofusedsamplewasrecordedinduringXPSinvestigationasshowninFigure6-2. TheanalysisofspectrapresentedinFigure6-2wereperformedby11point,2ndorder, Savitsky-GolaysmoothingfollowedbyaShirleybackgroundsubtraction.Thissetthe endsofthespectrumtoazerobaselineandthenthespectrawerenormalized.Thetwo spectrawereimportedobtainedfromcleanPtand3MLmonolayerofatomic oxygenonPtfromdatapresentedbyShumbera etal. 220 XPSdatadoesindicate oxideformationinthe1to3MLrange. ItisworthnotingthatthePt4fshoulderfromthe3MLoxideissmallbecausethe electronkineticenergyforthatpeakislarge1300eVwhenusingalaboratoryX-ray sourcewhichmaybeduetoreducedsurfacesensitivityatlowerbindingenergy. TEMwasappliedtostudyagglomerationofcatalystparticles;high-resolutionTEM monogramspresentedinFigure6-3haveshowedbiggerPtparticlesizeincaseofused MEAascomparedtofreshone.IntheTEMimagesofcross-sectionofMEAsmigration ofPtparticlesfromcathode-membraneinterfacetomembranewasobserved.TheTEM imageofcross-sectionoffreshandusedMEAsarepresentedinFigure6-4.Changesin interfaceofthecatalyst-membranewereevident. Thedecreaseinthesurfaceareacouldbeduetocombinedeect 101 ofimetal catalystclusteragglomerationoriilossofsupportparticlesandmetalclusterfrom thecatalystlayer.Duetoweakbondingofplatinumparticleswiththecarbonsupport, theformationofagglomeratesofthecatalystparticlesarepossible.Thedecreased 117

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Figure6-1:Full-scanXPSspectrumoftheusedsamplegeneratedatpassenergy89.45 eV.XPSscansweretakenwiththePHI5100ESCAsystembyPerkin-Elmeravailableat MAICintheUniversityofFlorida.X-raysourcewasMganodewithaworkfunction4.8 eV.Thesamplewasscannedat300wattspowerinenergyrangeof1000-0eVbinding energywithastepof0.5eVand30mSec/step. 118

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Figure6-2:Highresolutionperformedatpassenergyof22.36eVoftheXPSspectra onPtpeaks.XPSscansweretakenwiththePHI5100ESCAsystembyPerkin-Elmer availableatMAICintheUniversityofFlorida.X-raysourcewasMganodewithawork function4.8eV.Thesamplewasscannedat300wattspowerinenergyrangeof1000-0eV bindingenergywithastepof0.5eVand30mSec/step. a b Figure6-3:TEMimagesofcathodesurfaces.TEMstudywasperformedwithaJOEL JSM-2010FFieldEmissionElectronMicroscopeavailableatMAICintheUniversityof Florida.TheTEMmicrographsofcathodesurfacesweretakenat200kVaccelerating voltageinbrighteldmode;afreshsample;andbusedsample. 119

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a b Figure6-4:TEMimagesofcross-section.TEMstudywasperformedwithaJOELJSM2010FFieldEmissionElectronMicroscopeavailableatMAICintheUniversityofFlorida. TheTEMmicrographsweretakenat200kVacceleratingvoltageinbrighteldmode;;a freshsample;andbusedsample. surfaceareahasalsobeenattributedtotheplatinumdissolutionandredepositingatthe catalyst/ectrolyteinterface. 100 Themigrationoftheplatinumparticlestothemembrane interfacehasalsobeenreported. 94 Oncethecatalystparticlehasmigratedintothe membrane,itwouldlosetheelectricalcontactfromthecatalystlayer,whichcouldalso causethelossoftheelectrochemicalactivesurfacearea. TheSEMimagesofMEAcrosssectionsarepresentedinFigure6-5,inwhichthe morphologychangesintheinterfaceofelectrode-membranecanbeclearlyseen.Change insurfacefeatureswasobservedintheSEMimagesofsurfacethefreshFigure6-5a andtheusedFigure6-5bcatalystlayer.Thesetypeofchangeshavebeendescribedas mud-crackingandsurfaceerosionandhavebeenexplainedasaresultofcatalystparticle orrecastNaonionomerlossfromthecatalystsurfaceduetoparticledissolution. 101 6.3.2EuentAnalysis ICP-MSwasusedtoanalyzetheeuentfromthecathodeofthefuelcellunder operationatdierentpointsalongthepolarizationcurve.AtraceamountofPtwas 120

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a b Figure6-5:SEMmicrographsofcathodecross-sectionweretakenat15kVaccelerating voltage.Thecross-sectionofthebothfreshandusedMEAwascutwithsharprazorand thesampleswerecoatedwithAu-Pd;afreshsample;andbusedsample. estimatedatalevelof15ppbfortheusedsampleagainst6ppbforblanksample. Thisresultisinconsistentwiththeliterature.Xie etal. havealsoobservedPtinthe cathodeeuentbyICP-MS,andhaveattributedthisresulttoPtdissolution. 101,100 The dissolutionisconsistentwithreactionschemeproposedbyDarling etal. 10 whichsupports theformationoftheplatinumoxideasanintermediate. 6.3.3ElectrochemicalResponse Theperformanceofthefuelcellwasalsoinvestigatedwithtimeinformofpolarizationcurvesandimpedanceresponses.AspresentedinFigure6-6,theasharpdecrease inthecurrentdensitywasobservedwithtimeespeciallyapparentintheohmicandmass transportregimesofthepolarization. Theimpedanceresponseobtainedat0.2A/cm 2 ispresentedinFigure6-7.Anoverall increaseintheimpedancewasrecordedandalsothedierentfeaturesintheimpedance spectrawereobserved.Theeectofthemicrostructuralchangesduetodeactivationof thecatalystlayercanberelatedtotheobservedperformancelossinthepolarization curveandhigherimpedanceseenfortheusedsample.Furthermore,interfacialcapacitance wasestimatedfortheimpedancedatapresentedinFigure6-7followingtheprocedure describedinChapter8.Theinterfacialcapacitanceforthefreshsamplewasfoundas 121

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Figure6-6:Polarizationcurvegeneratedfromthesteady-statemeasurementfordierent timewith850CforH 2 asreactantattheanodeandairasoxidantatcathode.Theanode reactantstreamandcelltemperaturesweresetat40 0 Candthecathodereactantstream temperatureat35 0 C.Thefuelcellwasassembledwithaserpentineowchannel,anda uniformporousGDL. 122

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Figure6-7:Impedanceresponsescollectedatat0.2A/ cm 2 asafunctionoftimesafunctionoftimewith850CforafunctionoftimeforH 2 asreactantattheanodeandairas oxidantatcathode.Theanodeandthecelltemperaturesweresetat40 Candthecathodetemperatureat35 C.Thefuelcellwasassembledwithaserpentineowchannel,and auniformporousGDL. 0.078against0.045F/cm 2 fortheusedsample.Theobserveddecreaseintheinterfacial capacitancecanattributedtodecreaseinelectrochemicalareaduetoprocessessuchas PtOoxideformation. 123

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CHAPTER7 DETECTIONOFONSETOFFLOODING Impedancespectroscopyinconjunctionwiththemeasurementmodelanalysis wasusedtogainaninsightintotheproblemofoodingwhichadverselyaectsthe performanceofthefuelcell.Theapproachdemonstrateshowthestochasticcharacter ofoodingmaybeexploitedtodetectonsetofoodingwithouttheneedtoregress impedancespectra.Theresearchpresentedhaspotentialtogiveguidelinesforecient fuel-celloperation. 7.1Introduction Floodingincreasestheresistanceassociatedwiththegasdiusionlayerandmay evenblockowchannels,reducingtheavailabilityofoxygen. 149 Condensedwatermaybe removedbygasow.Thus,changesinreactantowchanneldesignhavebeenproposedto reducetheooding. Theobjectofthepresentworkwastoexplorehowthestochasticcharacterofooding canbeexploitedtoimprovesensitiveofimpedancespectroscopytodetectonsetof ooding.Impedancemeasurementswereperformedasafunctionofdierentparameters suchascurrentdensity,temperature,andtime.Acomprehensivemodelforbase-level noiseinimpedancemeasurementsfornormalconditionsnon-oodedwasdevelopedby ameasurementmodelanalysis, 124,125,221,222,194 andstochasticerrorswerealsoassessedby transientxed-frequencymeasurements.Acomparisonoftheactualnoisetothebase-level noisewasusedtodetectonsetofooding. 7.2Results Theinuenceofoodingontheoperationofthefuelcellwasinvestigatedusingimpedancespectroscopy.Theresultsoffrequencyscanandsingle-frequencytimedependentmeasurementsarepresentedinfollowingsections. 7.2.1ImpedanceResponse AtypicalimpedanceresponseispresentedinFigure7-1withcurrentdensityasa parameter.Thesizeoftheintermediate-frequencyandthelow-frequencyarcsincreased 124

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Figure7-1:Impedancedatarecordedwiththe850Cwithappliedcurrentdensityasa parameter.Theanode,cathode,andcelltemperaturesweresetto50 C. Figure7-2:Impedancedatarecordedwiththe850Cwithappliedcurrentdensityasa parameter.Theanode,cathode,andcelltemperaturesweresetto70 C. withincreasingcurrentdensity,aneectwhichwassuggestedintheliterature 12,157 tobe duepartiallytoooding.Theimpedancespectrawererelativelysmoothforlowcurrent densities;however,thespectrahavesignicantscatterathighercurrentdensitieswhere oodingwasprobable.Thescatterwasparticularlyevidentatlowfrequency,where thespectrashowjumpsinvaluewhichmaybeassociatedwithremovalofcondensed water.Similarresultswereobservedatothertemperatures.Theimpedancemeasured at70 CispresentedinFigure7-2withcurrentdensityasaparameter.Herealsothe impedancedatahavegreaterdegreeofscatterathighercurrentdensities,andthisscatter isparticularlyevidentatlowerfrequencies. 125

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a b Figure7-3:Single-frequencyImpedancemeasurementsrecordedat0.1Hz,70 C,and1.4 A/cm 2 asfunctionsoftime:arealpart;andbimaginarypart. 7.2.2StochasticErrorinImpedanceResponse Thestandarddeviationsofthestochasticerrorswereestimatedfrombothimpedance spectraandsingle-frequencytransientsfordry,ooded,andnon-oodedconditions. 7.2.2.1Sensitivitytoooding Theimpedancewasrecordedasafunctionoftimefordierentcurrentdensitiesand xed-frequencies.Forexample,therealandimaginarypartsofimpedanceat0.1Hzand 1.4A/cm 2 arepresentedasfunctionsoftimeinFigures7-3aand7-3b,respectively. Thestandarddeviationsintheimpedancedatawerecalculatedusingamovingaverage methodtoaccountforthesystematicchangesshowninFigure7-3.ThestandarddeviationsfortherealandimaginarypartsoftheimpedanceresponsearepresentedinFigure 7-4aforameasuredfrequencyof100HzandinFigure7-4bforafrequencyof1Hz. Atlowfrequencies,Figure7-4b,thestandarddeviationoftherealpartoftheimpedance isclearlylargerthanthatoftheimaginarypart.ThesolidlinegiveninFigure7-4representsthemodelvalueforthestandarddeviation,developedinasubsequentsectionfor non-oodedconditions. Thestandarddeviationsfortherealpartoftheimpedancearepresentedasa functionofcurrentdensityinFigure7-5forfrequenciesof0.1,10,and100Hz.The 126

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a b Figure7-4:Thestandarddeviationofthesingle-frequencyImpedancemeasurements recordedat1.4A/cm 2 and70 Casfunctionsoftime:aatafrequencyof100Hz;andb atafrequencyof1HzaspresentedinFigure7-3.Thesolidlinerepresentstheempirical modeldevelopedfortheerrorstructuregivenbyequation7{1. Figure7-5:Thestandarddeviationsfortherealpartoftheimpedanceasafunctionof currentdensitywithfrequencyasaparameterforcelloperationat70 C. 127

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stochasticerrorsintheimpedanceincreasedwithincreasingcurrentdensity,inparticular forthelowerfrequenciesof0.1and10Hz.Thestandarddeviationatlowerfrequenciesare higherthanthatathigherfrequenciesforanygivencurrentdensity. Thestatisticalnatureoftheerrorstructuremaybeusedtoexplainthelarger standarddeviationobservedatlargercurrentdensities.AsshowninFigure7-4b, thestandarddeviationoftherealpartoftheimpedanceat1Hzwasmuchhigheras comparedtoimaginarypart.TheresultspresentedinFigure7-4aindicatethatat 100Hz,thestandarddeviationofrealandimaginarypartsoftheimpedancewerealso unequal,buttheimaginarypartoftheimpedanceseemstohavethelargerstandard deviation.ForcausalsystemswhichsatisfytheKramers-Kronigrelations,thestandard deviationintherealandimaginarypartsshouldbeequal. 223 Theliteratureindicates that,atlowfrequencies,therealpartoftheimpedanceismoresensitivetoooding; 12,116 therefore,thehigherstandarddeviationoftherealpartoftheimpedanceobservedatlow frequenciesmaybeattributedtoonsetofooding. 7.2.2.2Baselineerrorstructure Toestablishabaselineerror-structuremodelforthestandarddeviationofimpedance measurementsintheabsenceofooding,ameasurementmodelanalysis 124,125,221,194 was appliedtoalargesetofreplicatedimpedancedata.Themeasurementmodelwasused toltersmallsystematicchangesfromonemeasurementtotheother.Thestandard deviationsforimpedanceresponserecordedat0.4A/cm 2 ,presentedinFigure7-6,were smallerthanthoseobservedatbothlargerandatsmallercurrentdensities.Therealand imaginarypartsoftheimpedancewerestatisticallyindistinguishableatallfrequencies, inagreementwithexpectationsfordatathatareconsistentwiththeKramers-Kronig relations. Themodelforerrorstructuredevelopedinpreviousworkforabroadvarietyof electrochemicalandelectronicsystems 135,210 didnotprovideagoodrepresentationof theerrorstructurepresentedinFigure7-6.Thefailureofthegeneralmodeltoapply 128

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Figure7-6:Standarddeviationsfortheimpedancedataobtainedatacurrentdensityof 0.4A/cm 2 .Thesolidlinerepresentstheempiricalmodeldevelopedfortheerrorstructure givenbyequation7{1.Thedashedlinesrepresenttheasymptoticbehaviorofthemodel athighandlowfrequencies. tothepresentdatawasattributedtodierencesintheparametersusedtomakethe measurement.Anempiricalmodelwasfoundtofollowtheform r = j = c + j Z r ; max j af )]TJ/F23 7.9701 Tf 6.586 0 Td [(b {1 where a =9 10 )]TJ/F21 7.9701 Tf 6.586 0 Td [(5 b =0 : 695,and c =3 : 5 10 )]TJ/F21 7.9701 Tf 6.587 0 Td [(5 .Themodelcanberationalizedby examinationofthestandardformulaforpropagationofstochasticerrors,whichcanbe writtenforimpedanceas 2 Z = 2 I [ @Z @ I ] 2 + 2 V [ @Z @ V ] 2 {2 where I ,and V areperturbationsincurrent,andpotentialrespectively,and Z isthe impedancegivenas Z = V I {3 129

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a b Figure7-7:Impedancemeasurementrecordedat0.4A/cm 2 and1Hzasfunctionsoftime at70 C:arealpart;andbimaginarypart. Equation7{2canbewrittenas 2 Z = 2 I [ V I 2 ] 2 + 2 V [ 1 I ] 2 {4 or 2 Z = 2 I I 2 Z 2 + 2 V [ 1 I ] 2 {5 Forgalvanostaticmodulationatxedamplitude,equation7{5takestheform Z = B j Z j + C {6 where C ,and B areconstants. Theerrorstructureidentiedforimpedancespectracanbecomparedtothat obtainedforsingle-frequencytransientmeasurementssuchaspresentedinFigure7-7 forimpedancedatacollectedat0.4A/cm 2 and1Hz.Thestandarddeviationsforthe realandimaginarypartsoftheimpedanceresponsearepresentedinFigure7-8afor ameasuredfrequencyof100HzandinFigure7-8bforafrequencyof1Hz.Theerror structuremodelrepresentedbyequation7{1isingoodagreementwiththestandard deviationsobtainedbytransientsingle-frequencymeasurements.At100Hz,Figure78a,thestandarddeviationoftherealandimaginarypartsoftheimpedanceareequal; 130

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a b Figure7-8:Thestandarddeviationofthesingle-frequencyImpedancemeasurements recordedat0.4A/cm 2 and70 Casfunctionsoftime:aatafrequencyof100Hz;andb atafrequencyof1HzaspresentedinFigure7-7.Thesolidlinerepresentstheempirical modeldevelopedfortheerrorstructuregivenbyequation7{1. however,asshowninFigure7-8b,thestandarddevaitionsforrealandimaginaryparts arenotequalatafrequencyof1Hz.Thisresultsuggeststhat,evenatacurrentdensity of0.4A/cm 2 ,wheretheerrorstructurewasthesmallest,someoodingmaybetaking place. Equation7{1providedagoodrepresentationoftheimpedanceerrorstructure obtainedatacurrentdensityof0.4A/cm 2 underabroadvarietyofconditions.Theerror structurefortheimpedanceresponsecollectedatdierenttemperaturesispresentedin Figure7-9aandtheinuenceofanode/cathodeback-pressureisexploredinFigure 7-9b.Themodelprovidedagoodrepresentationoftheerrorstructureforallcases consideredinFigure7-9.Accordingly,equation7{1wasusedtorepresentthebase-level standarddeviationformeasurementsunaectedbydryingoroodingconditions. 7.2.2.3Detectionofoodedconditions Impedancespectrawereobtainedatdierentcurrentdensities.Thestandard deviationsobtainedatlargercurrentdensitiesarecomparedinFigure7-10tothevalues obtainedat0.4A/cm 2 .Thestandarddeviationsobtainedforcurrentdensitiesof1.0and 131

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a b Figure7-9:Standarddeviationsfortheimpedancedataobtainedatacurrentdensityof 0.4A/cm 2 :awithsystemtemperatureasaparameter;andbat70 Cwithanode/cathodeback-pressureasaparameter.Thesolidlinerepresentstheempiricalmodelforthe errorstructuregivenbyequation7{1. Figure7-10:Standarddeviationsfortheimpedancedataobtainedatacurrentdensities of0.4,1.0,and1.4A/cm 2 .Thesolidlinerepresentstheempiricalmodelfortheerror structuregivenbyequation7{1. 132

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Figure7-11:Normalizedstandarddeviationsfortherealpartoftheimpedancecalculated fromthedatashowninFigure7-3asafunctionofcurrentdensitywithfrequencyasa parameter. 1.4A/cm 2 areclearlylargerthanthatpredictedbyequation7{1.Thediscrepancymay beattributedtostochasticprocesseswithinthecellsuchasassociatedwithooding. ThestandarddeviationspresentedinFigure7-5werenormalizedbythebasestochasticerrorslevelcalculatedusingtheerrorstructurepresentedbyequation7{1. TheresultfortherealpartoftheimpedanceispresentedinFigure7-11.Asshownin Figure7-11,thestandarddeviationoftheimpedancedataincreasedwithanincreasein theoperatingcurrent.Theincreasednoiselevelsareseenatafrequencyof100Hzaswell asatlowerfrequencies.Atlargecurrentdensitiesandatlowfrequencies,thestandard deviationcalculatedfortherealpartoftheimpedancewasmorethan20timesthat obtainedintheabsenceofooding.Thestandarddeviationoftheimaginarypartofthe impedancehadnocleardependencyonooding.Thestandarddeviationoftherealpart particularlyatlowfrequency,however,canbeusedtodetectonsetofooding. 133

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Figure7-12:TheimpedancedatarecordedusingtheMEAwithauniformGDL.The anode,thecathode,andcelltemperaturesweresetat50 C. SimilarexperimentsandanalysiswereperformedontheMEAwithauniformGDL. TheimpedanceresponseispresentedinFigure7-12withcurrentdensityasaparameter. Thescatteringathighercurrentdensitieswasmoreevidentthanobservedforexperiments usingthenon-uniformGDL.Transientsingle-frequencyimpedancemeasurementswere usedtoobtainthestandarddeviationsforrealandimaginarypartsoftheimpedance. ThestandarddeviationfortherealpartoftheimpedanceispresentedinFigure7-13as afunctionofcurrentdensityforfrequenciesof0.1,10,and100Hz.Thebase-lineerror structuremodelusedtonormalizethedatawascalculatedatacurrentdensityof0.2 A/cm 2 7.2.2.4Detectionofdryconditions ThestochasticerrorsforsmallcurrentdensitiesareshowninFigure7-14forthe MEAwithanon-uniformporedistribution.Theempiricalmodelgivenbyequation7{ 1providedagooddescriptionforthebehavioratacurrentdensityof0.4A/cm 2 ,but theobservederrorsaremuchlargerforlowercurrentdensitieswheredryconditionsare anticipated.ThisresultisconsistentwiththeexperimentalobservationsofSchneider et al. 155 whoreportimpedancescanswithlargescatteratlowfrequenciesfordryconditions. Thestandarddeviationoftherealpartparticularlyatlowfrequency,however,canbe usedaswelltodetectthepresenceofdryconditions. 134

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Figure7-13:NormalizedstandarddeviationsfortherealpartoftheimpedanceasafunctionofcurrentdensitywithfrequencyasaparameterfortheMEAwithauniformpore distribution.Theanode,thecathode,andcelltemperaturesweresetat50 C. Figure7-14:Standarddeviationsfortheimpedancedataobtainedatacurrentdensities of0.02,0.1,and0.4A/cm 2 .Thesolidlinerepresentstheempiricalmodelfortheerror structuregivenbyequation7{1.Theanode,thecathode,andcelltemperatureswereset at70 C. 135

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7.3Discussion Duetoitsinuenceonmasstransferandkinetics,theonsetofoodinginthefuelcell canbeidentiedbyadecreaseincellpotentialatxedcurrentoradecreaseincurrent atxedpotential.Similarly,theonsetofoodingcanbeidentiedbyanincreaseinthe cellimpedance.Inthepresentwork,theincreaseinthelow-frequencycellimpedance associatedwithoodingwasontheorderof10percent.Theincreaseof10percentinthe cellimpedancewasaccompaniedbyanincreaseinthestandarddeviationoftherealpart oftheimpedanceby2000or3000percent. Theincreaseinstochasticerrorsintheimpedancemeasurementcanbeattributedto therandomcharacteroftheoodingprocessinwhichdropletsofwaterareformedand thenremovedbygasow.Infact,theincreaseinstochasticerrorsprovidesverication thattheincreasedcellimpedancewasatleastpartiallyduetoooding.Impedance spectroscopyhasbeenshowntoprovideamoresensitiveassessmentofcellcondition thansteady-statemeasurementsofcellpotentialandcurrent.Thedicultywithusing impedancedirectlytodetectoodingisthatabaselinevaluefortheimpedancemustbe establishedintheabsenceofooding.Thisbaselinemust,however,changewithtimedue tosystematicchangestocatalystandmembranepropertiesthatarenotassociatedwith ooding.Thus,abaselineestablishedwhenacellisrstcommissionedwillnotbevalid throughoutthelifetimeofthecell. Incontrast,themodelgivenbyequation7{1forthestandarddeviationofthe impedanceshouldbeaectedlargelybyinstrumentalsettings,and,solongasthe impedanceismeasuredinthesameway,abaselineestablishedforthestandarddeviationofimpedancemeasurementsintheoodedconditionshouldbevalidthroughoutthe lifetimeofthecell.Inaddition,thechangeinthestandarddeviationofthemeasurement causedbyoodingis100timeslargerthanthecorrespondingchangeinthevalueofthe impedance.Thus,assessmentofthestandarddeviationofimpedancemeasurementswill provideamoresensitiveindicatorfortheonsetofoodinginaPEMfuelcell. 136

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Figure7-15:Normalizedstandarddeviationsfortherealpartoftheimpedancemeasured at0.1HzforfuelcellscontainingtwodierentMEAsasafunctionofcurrentdensity.The experimentsfortheuniformMEAwereperformedat50 C,andtheexperimentsforthe nonuniformMEAwereperformedat70 C. ThestandarddeviationoftheimpedancemeasurementsweresensitivetothepropertiesoftheMEAusedintheexperiment.Acomparisonofthenormalizedstandard deviationsfortherealpartoftheimpedanceispresentedinFigure7-15withGDLpropertiesasaparameter.TheexperimentsfortheuniformMEAwereperformedat50 C, andtheexperimentsforthenonuniformMEAwereperformedat70 C.Thenormalized standarddeviationincreasedatlowercurrentdensitiesfortheGDLwithauniformpore distribution.ThevaluewasclosertounityoverabroaderrangefortheGDLwitha nonuniformporedistribution.Theresultsareconsistentwiththeobservationthatalarger maximumcurrentdensitycouldbeobtainedwiththenonuniformGDL.Micro-macro porousGDLsarereportedtoprovidebetterwatermanagement. 64{66 Theincreasein normalizedstandarddeviationatlowcurrentdensitiesobservedforthenon-uniformGDL islikelyduetodryingofthemembrane. 152,12 Similarexperimentswerenotperformedfor theuniformGDL. 137

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CHAPTER8 EVALUATIONOFINTERFACIALCAPACITANCE GraphicalmethodswereusedtoextractvaluesofCPEparametersandinterfacial capacitancefromimpedancedatacollectedonaPEMfuelcell.Theimpedancedata wererecordedasafunctionofcurrentdensity,time,temperature,backpressure,and owchannelandgasdiusionlayerdesign.Thevalueoftheinterfacialcapacitancewas reducedwhenthecellwasoperatedunderdryoroodedconditions.Theinterfacial capacitancedecreasedwithtimeoveratimescaleconsistentwiththeapproachtoasteady state.Inadditiontoprovidinganinsightintophysicalprocesses,theparametersobtained fromgraphicalmethodscanbeusedformodelreductionwhenregressingimpedance data.Themethodologypresentedcanbeappliedtoanyelectrochemicalsystemonwhich impedancemeasurementscanbeconducted. 8.1Introduction UseofCPEparametersisfrequent,thoughparametersestimatedbyttingcircuit modelstoimpedancedataarenotunique.TheobjectofthisworkwastousethegraphicalmethodsdescribedbyOrazem etal. 224 toevaluatetheinuenceofoperationand designparametersontheinterfacialcapacitanceofaPEMfuelcell.ThetransientbehaviorofCPEparameterswasalsoinvestigated.Theparametersobtainedbythegraphical methodswereusedtoexploreprocessessuchasooding,drying,andcatalystdeactivation inthefuelcell. 8.2Results TypicalimpedanceresultsarepresentedinFigure8-1withcurrentdensityasa parameter.ThemeasurementmodeldevelopedbyAgarwal etal. 124,125,221,222 wasusedto analyzetheerrorstructureoftheimpedancedata. 194,225 AsshownbyRoyandOrazem, 194 datacollectedaboveafrequencyof1kHzwereinconsistentwiththeKramers-Kronig relations.Thisinconsistencywasattributedtoinstrumentalartifacts.Onceasteady operationhadbeenachieved,thedatacollectedatfrequenciesaslowas1mHzwerefound tobeconsistentwiththeKramers-Kronigrelations.Datafoundtobeinconsistentwith 138

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Figure8-1:Impedanceresponserecordedat70 Cwithcurrentdensityasaparameter. Thefuelcellwasassembledwithanon-uniformGDLandaninterdigitatedowchannel. theKramers-Kronigrelationswereremovedfromthedatasetusedforfurtheranalysis. Forthetransientmeasurementsobtainedat0.02A/cm 2 seeFigure8-11,thedataat frequenciesabove500HzwereinconsistentwiththeKramers-Kronigrelations.Forall othermeasurements,thedatawereconsistentwiththeKramers-Kronigrelationsat frequenciesbelow1kHz. 8.2.1ApplicationofAsymptoticGraphicalAnalysis CPEparameterswereestimatedfordatafoundtobeconsistentwiththeKramersKronigrelationsusingthegraphicalmethodsillustratedbyOrazem etal. 224 TheCPE exponent wascalculatedfromtheslopeathighfrequencyofalogarithmicplotofthe absolutevalueoftheimaginarypartoftheimpedanceasafunctionoffrequency,shown inFigure8-2a.Theresultingvalueof ispresentedinFigure8-2basafunctionof currentdensity.Anincreasein wasobservedwithanincreaseincurrentdensity. Giventhevalueof presentedinFigure8-2b,theCPEcoecient Q e couldbe calculatedfrom Q e =sin 2 )]TJ/F15 11.9552 Tf 9.299 0 Td [(1 Z j f {1 139

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a b Figure8-2:RepresentationofthegraphicalanalysisofthedatapresentedinFigure8-1 toobtaintheCPEexponent :athemagnitudeoftheimaginarypartoftheimpedance asafunctionoffrequencywithcurrentdensityasaparameter;andbCPEexponent obtainedfromtheslopeofpartaathighfrequencies. asproposedbyOrazem etal. 224 where Z j istheimaginarypartoftheimpedance,and f isthefrequencyinunitsofHz.Thevalueof Q e ispresentedinFigure8-3aasa functionoffrequencywithcurrentdensityasaparameter.Thefrequencydependenceof theapparentCPEcoecient,evidentatfrequenciesbelow50Hz,iscausedbyFaradaic andtransportprocesses.Faradaicandtransportprocesseshavenegligibleinuenceat higherfrequencies.Thevalueof Q e wasobtainedbyestimatingthehigh-frequency asymptoteofFigure8-3abycalculatingtheaverageofthe10valuesatthehighest frequencies. Theinterfacialcapacitance C e wascalculatedby C e =[ Q e R 1 )]TJ/F23 7.9701 Tf 6.587 0 Td [( e ] 1 {2 asderivedbyBrug etal. 158 where R e istheelectrolyteresistancecalculatedfromthe high-frequencypartoftheimpedancedatapresentedinFigure8-1.Inacomparison ofexpressionsdevelopedbyHsuandMansfeld 226 andBrug etal. 158 Huang etal. 171 foundthatequation8{2providedanexcellentassessmentofinterfacialcapacitancefor systemsforwhichtheCPEbehaviororiginatedfromnonuniformcurrentandpotential distributionsalongtheelectrodesurface.Valuesofinterfacialcapacitance C e obtained 140

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a b Figure8-3:RepresentationofthegraphicalanalysisofthedatapresentedinFigure8-1 toobtaintheCPEcoecient Q e andtheinterfacialcapacitance C e :aCPEcoecient obtainedfromequation8{1;andbtheinterfacialcapacitanceobtainedfromequation 8{2. fromequation8{2arepresentedinFigure8-3basfunctionsofcurrentdensity.A decreasein C e wasobservedwithincreasingcurrentdensity. Toinvestigatetheinuenceofthestate-of-healthdryingandoodingofthefuel cell,similaranalyseswereperformedoverabroaderrangeofcurrentdensitiesandas afunctionoftime.Thecorrespondingvaluesobtainedfor Q e arepresentedinFigure 8-4withtimeasaparameter.TheCPEcoecient Q e wassignicantlyloweratsmall currentdensities,wherelocalizeddryingoftheMEAcouldbeexpectedduetoreduced productionofwateratthecathodecoupledwithredistributionbyelectro-osmosis.The CPEcoecientwasalsoreducedatlargecurrentdensitieswhichareassociatedwith ooding.Thelargestvalueof Q e wasfoundatintermediatecurrentdensities.Atall currentdensitiesforwhichtheeectoftimeon Q e wasexplored,thevalueof Q e decreasedwithtime. Thecorrespondingvaluesforinterfacialcapacitance C e ,obtainedfromequation 8{2,arepresentedinFigure8-5asafunctionofcurrentdensitywithtimeasaparameter.Thebehavioroftheinterfacialcapacitancewasconsistentwiththatfoundfor theCPEcoecient.Itshouldbenoted,however,thatthenumericalvalueforinterfacial capacitancereportedinFigure8-5issignicantlydierentfromthenumericalvalueofthe 141

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Figure8-4:CPEcoecient Q e asafunctionofcurrentdensitywithtimeasaparameter. TheimpedancedatawereobtainedundertheconditionsdescribedforFigure8-1. Figure8-5:Theinterfacialcapacitance C e ,obtainedfromequation8{2,asafunctionof currentdensitywithtimeasaparameter.Theimpedancedatawereobtainedunderthe conditionsdescribedforFigure8-1. 142

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a b Figure8-6:ElectrochemicalparametersobtainedforthedatapresentedinFigures8-4and 8-5asafunctionofcurrentdensitywithtimeasaparameter:aCPEexponent ;andb Ohmicresistance R e CPEcoecientpresentedinFigure8-4.Thevaluesof Q e are4to10timeslargerthan thevaluesof C e Thedierencebetweenthevaluesof Q e and C e iscloselyrelatedtothevalues obtainedfortheCPEexponent presentedinFigure8-6a.Athighandlowcurrent densities, approachesvaluescloseto0.8.Intheseregions, Q e isabout4timeslarger than C e .Atintermediatecurrentdensities, hasvaluesnear0.6,and Q e isabout10 timeslargerthan C e .TheOhmicresistance,showninFigure8-6b,alsoplaysarole incalculationofcapacitancefromequation8{2.Asignicantincrease R e wasobserved atdryingandoodingconditions.Theobservedincreasein R e atdryingandooding conditionsareconsistentwithobservationsreportedbyBarbir etal. 152 8.2.2EectofOperatingParameters TheinuenceoftemperatureontheimpedancemeasurementsispresentedinFigure 8-7fordataobtainedatacurrentdensityof0.5A/cm 2 .Theimpedancewassmallerat elevatedtemperatures,suggestingimprovedcellperformance.Theproceduredescribedin theprevioussectionwasusedtoobtaintheinterfacialcapacitancepresentedinFigure8-8 asafunctionofsystemtemperature.Anincreaseininterfacialcapacitancewasobserved 143

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Figure8-7:Impedanceresponserecordedatacurrentdensityof0.5A/cm 2 withsystem temperatureasaparameter.TheexperimentalsystemwasthesameasdescribedinFigure8-1. Figure8-8:Theinterfacialcapacitance C e ,obtainedfromequation8{2,asafunctionof systemtemperatureforthedatapresentedinFigure8-7. 144

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Figure8-9:Theinterfacialcapacitance C e ,obtainedfromequation8{2,asafunction ofbackpressureappliedforboththecathodeandtheanode.Theimpedancedatawere recordedat0.7A/cm 2 at70 C.Theexperimentalsystemwasthesameasdescribedin Figure8-1. atelevatedtemperatures,whichmayaccountpartiallyforthebetterperformanceat highertemperatures. Asimilarinvestigationoftheinuenceofbackpressurewasperformed.Theresulting interfacialcapacitance,obtainedfromequation8{2,ispresentedinFigure8-9asa functionofbackpressureappliedforboththecathodeandtheanode.Theimpedancedata wererecordedat0.7A/cm 2 at70 C.Asignicantincreaseininterfacialcapacitancewas observedwithanincreaseinthebackpressurefrom0to2barg.Subsequentincreasesin backpressureresultedinonlysmallincreasesininterfacialcapacitance. 8.2.3EectofDesignParameters Impedancedatarecordedwithdierentcombinationsofowchannelsandgasdiusionlayerswerealsoanalyzedtoestimatetheinterfacialcapacitanceaspresentedin Figure8-10.TheinterfacialcapacitanceforMEAsassembledusingagasdiusionlayer withanonuniformporedistributionwassignicantlylargerthanthatobtainedforMEAs assembledusingagasdiusionlayerwithauniformporedistribution.Thisdierence maybeattributedtotheimprovedwatermanagementpropertiesofthegasdiusion 145

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Figure8-10:Interfacialcapacitanceasafunctionofcurrentdensityfordierentcombinationsofowchannelsandgas-diusionlayers.Theimpedancedatawererecordedat70 C. layerwithanonuniformporedistribution.Theinuenceofowchanneldesignwasmuch lesssignicant.ForMEAsassembledusingagasdiusionlayerwithanonuniformpore distribution,theinterfacialcapacitancewaslargerfortheinterdigitatedowchannel ascomparedtotheserpentineowchannel.Theobservationthatthevalueof C e was foundtobelargerwhenusingagasdiusionlayerwithanonuniformporedistribution isconsistentwiththeobservationthatthesesystemsyieldedalargerlimitingcurrent density. 8.2.4TransientBehavior Toexploretheinuenceoftime,sequentialimpedancespectrawererecordedfora varietyofoperatingconditions.TheresultinginterfacialcapacitanceisreportedinFigure 8-11asafunctionoftimewithoperatingandsystemconditionasaparameter. Theinterfacialcapacitancedecreasedwithtimeforallimpedancedata,butthe dependenceontimewassmallerthanwasobservedwithcurrentdensity.Thedecrease intheinterfacialcapacitancecanbeattributedtotheslowapproachtosteadystate 146

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Figure8-11:Interfacialcapacitanceasafunctionoftimewithoperatingandsystemconditionasaparameter.Theimpedancedatawererecordedat70 CusinganMEAwitha non-uniformGDL. operation,asreportedbyRoyandOrazem. 194 Therateofdecreasewassmallestfor currentdensitiesleastaectedbyooding.2A/cm 2 fortheserpentineowchannel and0.4A/cm 2 fortheinterdigitatedowchannel.Theinterfacialcapacitancewas smallestforthesystemaectedbylocalizeddrying.02A/cm 2 fortheinterdigitatedow channel.Theinterfacialcapacitancewassomewhatsmallerforthesystemaectedby ooding.0A/cm 2 fortheinterdigitatedowchannel. ThecorrespondingvaluesofCPEexponent arepresentedinFigure8-12.TheCPE exponentincreasedwithtimeforallimpedancedataandhadvaluesthatrangedbetween 0.57and0.8.Thevalueof waslargestforthesystemsmostlikelytobeaectedby oodingordrying. 8.3Discussion Systemparametersaretypicallyobtainedfromimpedancedatabyregressionof models.Accordingly,thevalueoftheparametersobtaineddependonthesuitabilityof themodelandonthequalityoftheregression.Thegraphicalmethodsemployedinthe presentworkprovideinformationthatislimitedtothehigh-frequencyportionofthe spectrum,wheretheFaradaicandtransportprocessesdonotinuencetheimpedance 147

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Figure8-12:CPEexponent Interfacial-capacitanceasafunctionoftimecorresponding totheresultspresentedinFigure8-11. response.Theadvantageofthegraphicalmethodsemployedhereisthattheparameter valuesdonotdependonthesuitabilityofthemodelandonthequalityoftheregression. ThevaluesoftheCPEparameters Q and canbeobtainedunequivocally;however,the relationshipbetweentheseparametersandtheinterfacialcapacitancerequiresamodel. TheformulasdevelopedbyBrug etal. 227 werefoundtogivegoodaccountingfor2-D distributions. 171 Asimilarvericationhasnotbeenprovidedfor3-Ddistributions,though theBrugformulahasbeeninvokedtodescribetherelationshipbetweenCPEparameters and3-Ddistributionsinoxides. 228 Thevaluesof wasfoundinthepresentworktorangebetween0.57-0.8,whichis consistentwiththevalueof0.8027reportedbyFouquet etal. 157 Thevalueof canbe expectedtoresultfromacombinedlateraldistribution,associatedwiththedistribution ofcurrentandpotentialalongtheowchannelsandbetweenlandandchannelareas,and anaxialdistributionassociatedwiththeporouscharacteroftheMEA.Thedecreased valueof atlowandhighcurrentdensitiesmaybeattributedtoincreasedheterogeneity createdbydryingorooding,respectively.Correspondingly,adecreaseinthevalueof C e wasfoundunderconditionsassociatedwithdryingandooding.Thecalculatedinterfacial 148

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capacitanceisusuallyscaledtoelectrochemicalactivesurfaceareaofcatalyst. 229 A decreaseineectivesurfaceareaofroughly60percentwasfoundunderdryingconditions, andadecreaseofroughlywasfoundunderoodingconditions. Thehighervalueestimatedfortheinterfacialcapacitancecouldcontributetothe improvedperformancesofthefuelcellatelevatedtemperature 4 andelevatedoperating pressure. 196 Thesensitivityofinterfacialcapacitancetopoorwatermanagementaccounts forthesmallvaluesofcapacitancewhenusingauniformGDL.Thecapacitancewas largerwhenusingamicro-macroporousGDL,whichisreportedtoprovidebetterwater management. 64{66 Thesharpdecreasein C e atlowcurrentdensitiesobservedforthe non-uniformGDLislikelyduetodryingofthemembrane. 152,12 Similarexperimentswere notperformedfortheuniformGDL.Theobservationofahighervalueoftheinterfacial capacitancefortheinterdigitatedowchannelisconsistentwithobservationofhigher currentdensitiesandbetterfuelcellperformanceascomparedtotheserpentineow channel. 4,200,206,207 Amoderatedecreaseinthevalueof C e withtimewasobserved. Theobserveddecreaseintheinterfacialcapacitancecanbeconvertedintoanequivalent decreaseintheelectrochemicalactivesurfaceareawithtime,whichcouldbeduetothe slowapproachtosteady-stateoperation. 194 149

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CHAPTER9 CONCLUSIONS Anintegralapproachcomprisedoferroranalysis,modelinterpretationsandvalidationsbasedonimpedanceresponseofthefuelcellwasemployedtoinvestigatefactors inuencingperformanceandlifetime.Useofimpedancetechniqueswasalsoexploredto gainaninsightintotheproblemofooding,dryinginthefuelcell.Theconclusionsare presentedinthefollowingsections. 9.1ErrorAnalysisofImpedanceResponse TheimpedancedataforthefuelcellwereanalyzedusingaVoigtmeasurementmodel. TheinductiveloopsfoundatlowfrequencywerefoundtobeconsistentwiththeKramerKronigrelationoncethefuelcellachievedsteady-stateoperation.Theformalismofthe measurementmodelerroranalysisprovidesameansfordeterminingwhetherasteady statehasbeenachieved. Thispartoftheworkconrmedthatthelow-frequencyinductiveloopscouldbe attributedtoprocessesoccurringinthefuelcell.Kramers-Kronigconsistentinductive loopswereobservedintheentirerangecurrentdensityofoperationofthefuelcell.The resultswereindependentoftheimpedanceinstrumentationused. 9.2InterpretationofImpedanceResponse Low-frequencyinductiveloopswereobservedinimpedancemeasurementsofthefuel cell.TheseloopswerefoundtobeconsistentwiththeKramers-Kronigrelationsandwere observedforallpartsofthepolarizationcurve.Threeanalyticimpedancemodelswere derivedfromconsiderationofspecicreactionsequencesproposedtotakeplaceinthe fuelcell.Themodelthataccountedonlyforhydrogenoxidationandoxygenreduction couldnotaccountforthelow-frequencyinductiveloopsobservedinexperimentaldata. Modelsthataccountedforadditionalreactions, i.e., formationofhydrogenperoxideand formationofPtOwithsubsequentdissolutionofPt,couldpredictlow-frequencyinductive loops.Thesemodelsweresupportedbycomplementaryexperiments,andtheresultsshow thateitherofthesereactionmechanismscouldaccountfortheexperimentallyobserved 150

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low-frequencyinductiveloops.Thesemodelscanalsobeusedtopredictsuchvariablesas thefractionalsurface-coverageoftheproposedintermediates. 9.3Ex-SituAnalysis Theformationofintermediatesintheproposedreactionmechanismswereconrmed byexperimentalinvestigationsincludingXPS,TEM,SEM,andICP-MSanalysis.The XPSstudiesindicatethatafter600hoursofuse,alayerofPtOwasformedequivalentto 3monolayer.Thesubstantialhydrogencrossoverthroughthemembraneestimatedbythe CVexperimentssupportsperoxideformation.Thus,bothreactionsequencesproposed inModels2and3arelikelyinthefuelcellunderstudy,andboththereactionsequences werefoundtoyieldlow-frequencyinductiveloopsintheimpedanceresponse.Thiswork suggeststhatquantitativeanalysisoflow-frequencyinductiveloopsmayprovideauseful characterizationofreactionswhichreducetheeciencyandoperatinglife-timeofthefuel cell. 9.4DetectingOnsetofFlooding Theoodingofgasdiusionlayerporesinthefuelcellhasbeenassociatedwith increasesintheinternalcellresistanceandintheimpedanceresponseofthefuelcell. Theformationandremovalofwaterdropletsisaninherentlystochasticprocesswhich increasesthestochasticerrorsobservedinimpedancemeasurements.Ameasurement techniqueorientedtowardsassessmentofthestochasticerrorscanthereforebeusedto identifytheonsetofooding.Inthepresentwork,impedancespectroscopywascoupled withameasurement-model-basederroranalysistodetectonsetofooding.Thismethod isparticularlyattractivebecauseitisextremelysensitiveandawell-denedbaseline stochasticerrorcanbeestablishedforthenon-oodingcondition. Theonsetofoodingwasexaminedfora5cm 2 PEMfuelcellwithaninterdigitated owchannel.Atlowcurrentdensities,theratiooftheobservedstandarddeviationtothe expectednon-oodedstandarddeviationwasclosetounity.Atlargercurrentdensities, theratiofortherealpartoftheimpedancebecamequitelarge,withonsetofooding 151

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evidentatcurrentdensitiesabove1A/cm 2 fortheMEAwithanon-uniformGDLandat currentdensitiesabove0.3A/cm 2 fortheMEAwithauniformGDL.Dryingwasevident atcurrentdensitiesbelow0.3A/cm 2 fortheMEAwithanon-uniformGDL. Theworkpresentedheredemonstratesthatthestochasticerrorstructureof impedancemeasurementsmaybeusedtodetectoperatingconditionsofthefuelcell whichinduceoodingordrying.Inthiscase,theoodingordryingphenomenacontributestochasticerrorswhicharesuperposedonthoseassociatedwiththeelectronic instrumentation. 9.5EvaluationofInterfacialCapacitance GraphicalmethodswereusedtointerpretimpedancespectraintermsofCPEparameters,andtheformulaspresentedbyBrug etal. 227 wereusedtoconverttheseinto eectiveinterfacialcapacitance.Theeectiveinterfacialcapacitancewassmallestatsmall andlargecurrentdensitiesandshowedamaximumvalueattheintermediatecurrent densities.Thedecreasesininterfacialcapacitancewithhighercurrentdensitycanbe attributedtoanexcessproductionofwaterresultinginooding;whereas,atlowcurrent density,theeectcouldbeattributedtodrying.Theinterfacialcapacitancewasdependentonowchannelconguration,GDLproperties,temperature,andbackpressure.The improvedperformanceandlargerinterfacialcapacitanceobservedfortheinterdigitated owchannelandthenon-uniformGDLcouldbeattributedtotheimprovedwatermanagementcapabilitiesofthesesystemdesigns.Asmallerinuenceoftimewasobserved whichcouldbeassociatedwiththelongtimerequiredtoachievesteady-stateoperation. 194 Theuseofgraphicalmethodstoextractphysicalpropertiesisunder-utilizedinthe fuelcellliterature.ThemethodprovidesunequivocalvaluesfortheCPEexponent theCPEcoecient Q ,andtheOhmicresistance R e .Theinterpretationoftheresulting parametersintermsofinterfacialcapacitanceis,however,lessclear.Moreworkisneeded toconrmthesuitabilityoftheBrugformulaforcombined2-D/3-Ddistributionspresent inthePEMfuelcell. 152

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CHAPTER10 FUTUREDIRECTIONS Recommendationsforthefutureresearchofthisworkarepresentedinthischapter. Togainbetterunderstandingintotheproposedmechanisms,thefollowingresearchplan canbeemployedasafuturedirectionofthisproject. 10.1ParameterEvaluation Theexperimentaldatacanberegressedtotheimpedancemodelsdevelopedto extractmeaningfulparameterssuchasrateconstantsforreactionkinetics,andtransport propertieslikediusivityofspecies.Moreover,otherinformationsuchasexchangecurrent density,andlimitingcurrentdensitycanalsobeevaluated. 10.2Euent,andMicrostructureAnalysis Moreworkneededtoprovideevidencetosupportordisproveproposedreaction mechanisms.ICP-MScanbeappliedtoestimateplatinumconcentration 94 intheeuent waterofthefuelcell.ICIonChromatographycanbeusedtoestimateuorideemission rateintheeuent.TheChemtricsTestKitcanbeusedtomeasurehydrogenperoxide concentration, 9 andtheOrionTestKitcanbeusedtomeasureuorideionconcentration intheeuentwater.Theinformationfoundfromthemicrostructuralanalysisandthe euentanalysiscanbeusedtovalidatethepropositionofthereactionmechanismsfor themodeldevelopment, e.g., theplatinumdissolutionandtheperoxideformation.The uorideionconcentrationinthefuelcelleuentwillgivetheinformationaboutlifetime ofthemembrane. 10.3One-DimensionalFlowChannel Thepseudo1-Dimensionalowchannelinvestigatedshouldbeanalyzedcomprehensivelytoimprovethedesignfurther.Improvedowchannelcanbeusedtocomparemodel andexperimentresultsinthesearchofkineticsandtransportparametersimportantto describethefuelcell. 153

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APPENDIXA:COMPUTATIONALALGORITHMFORMODEL1 r 1=0 : 135;[Electrolyteresistance] c =0 : 212;[Double-layercapacitance] o =0 : 5[symmetrycoecientforORR] h = )]TJ/F22 11.9552 Tf 11.955 0 Td [( o ;[symmetrycoecientforHOR] V =0 : 68;[operatingvoltage] F =96500;[Faradaysconstant] R =8 : 314;[Universalgasconstant] T =298;[Temperature] dh 2=9 10 )]TJ/F15 11.9552 Tf 7.085 -4.339 Td [(;[diusivityforoxygen] do 2=3 : 69 10 )]TJ/F15 11.9552 Tf 7.085 -4.338 Td [(12;[diusivityforhydrogen] delta =10 )]TJ/F15 11.9552 Tf 7.085 -4.338 Td [(6;[lmthickness] ko =2 : 63 10 )]TJ/F15 11.9552 Tf 7.084 -4.338 Td [(2;[RateconstantforORR] kh =3 : 6 10 )]TJ/F15 11.9552 Tf 7.085 -4.338 Td [(4;[RateconstantforHOR] iexp =[];[exportexperimentaldata] eexp =[];[exportexperimentaldata] Cmbulkh 2[denebulkconcentrationforhydrogen] Cmbulko 2[denebulkconcentrationforoxygen] O = ko exp )]TJ/F15 11.9552 Tf 9.299 0 Td [( o FV = RT ;[KineticexpressionforORR] H = kh exp )]TJ/F15 11.9552 Tf 9.298 0 Td [( h FV = RT ;[KineticexpressionforHOR] ilimh 2= : F: Dh 2 : Cmbulkh 2 := delta ;[limitingcurrentofhydrogen] ilimo 2= : F: Do 2 : Cmbulko 2 := delta ;[limitingcurrentofoxygen] A =2 : Kh 2 : F: Dh 2 : Cmbulkh 2 : exp bh 2 : vh 2;[lumpedparameterforHOR] B =4 : Ko 2 : F: Do 2 : Cmbulko 2 : exp )]TJ/F22 11.9552 Tf 9.299 0 Td [(bo 2 : vo 2;[lumpedparameterforORR] ih 2= A: ilimh 2 := A + ilimh 2;[currentfromHOR] io 2= B: ilimo 2 := B + ilimo 2;[currentfromORR] plot io 2 ;V; 0 0 ;[currentfromORR] 154

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iT = io 2;[currentatcathode] ih 2= iT ;[currentatanode] na = log iT := Kh 2 : Cmbulkh 2 : )]TJ/F15 11.9552 Tf 12.063 0 Td [( iT:=ilimh 2 :=bh 2;[equatingcurrentat cathodeandanode] VT = V )]TJ/F15 11.9552 Tf 11.955 0 Td [( iT: Reff + na ;[cathodeoverpotential] plot iT;VT; 0 )]TJ/F25 7.9701 Tf 9.299 4.338 Td [(0 ; plot iexp;eexp; 0 o 0 ; Rto =[ o F 2 )]TJ/F22 11.9552 Tf 11.955 0 Td [( O = RT ];[Charge-transferresistanceforORR] Rth =[ h F 2 H = RT ];[Charge-transferresistanceforHOR] p 0=2 Fkoexp )]TJ/F22 11.9552 Tf 9.299 0 Td [( o FV= RT ;[Mass-transferimpedanceforORR] q 0=2 Fkhexp )]TJ/F22 11.9552 Tf 9.299 0 Td [( h FV= RT ;[Mass-transferimpedanceforHOR] w = )]TJ/F15 11.9552 Tf 9.298 0 Td [(6: : 05:6;[Frequencyrange] w =10 : w ; p 1= Rto ; Kh 2= w delta 2 =dh 2;[tangenthyperbolicforHydrogen] th 2= tanh sqrt i Kh 2 := sqrt i Kh 2; Ko 2= w: delta 2 =do 2; to 2= tanh sqrt i Ko 2 := sqrt i Ko 2; A 1=1 := RtO 2+ ZDO 2 to 2;[lumpedparametersforHOR] C 1=1 := RtH 2+ ZDH 2 th 2;[lumpedparametersforHOR] p 2= p 0; q 1= Rth ; q 2= q 0; z 1= p 1 )]TJ/F22 11.9552 Tf 11.955 0 Td [(q 1 : p 2 )]TJ/F22 11.9552 Tf 11.956 0 Td [(q 2; z 2= z 1 := jwF 2 )]TJ/F22 11.9552 Tf 11.955 0 Td [(p 2 )]TJ/F22 11.9552 Tf 11.955 0 Td [(q 2; z 3= z 2+ p 1+ q 1+ jwc ; z 4=1 :=z 3; 155

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z = r 1+ z 4;[overallimpedance] zr = real z ; zi = imag z ; plot exzr; )]TJ/F22 11.9552 Tf 9.299 0 Td [(exzj; 0 o 0 daspect [111] y =[ zr ; zi ]; fid = fopen 0 M 1 EIS 90 :txt 0 ; 0 w 0 ; fclose fid ; 156

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APPENDIXB:COMPUTATIONALALGORITHMFORMODEL2 r 1=0 : 135;[Electrolyteresistance] c =0 : 212;[Double-layercapacitance] o =0 : 5[symmetrycoecientforORR] h = )]TJ/F22 11.9552 Tf 11.955 0 Td [( o ;[symmetrycoecientforHOR] V =0 : 68;[operatingvoltage] F =96500;[Faradayconstant] R =8 : 314;[Universalgasconstant] T =298;[Temperature] dh 2=9 10 )]TJ/F15 11.9552 Tf 7.085 -4.339 Td [(;[diusivityforoxygen] do 2=3 : 69 10 )]TJ/F15 11.9552 Tf 7.085 -4.338 Td [(12;[diusivityforhydrogen] dh 2 o 2=4 e )]TJ/F15 11.9552 Tf 11.955 0 Td [(15;[diusivityforperoxide] delta =10 )]TJ/F15 11.9552 Tf 7.085 -4.338 Td [(6;[lmthickness] ko =2 : 63 10 )]TJ/F15 11.9552 Tf 7.084 -4.338 Td [(2;[RateconstantforORR1] kh =3 : 6 10 )]TJ/F15 11.9552 Tf 7.085 -4.339 Td [(4;[RateconstantforHOR] kh 2 o 2=3 : 6 10 )]TJ/F15 11.9552 Tf 7.085 -4.339 Td [(4;[RateconstantforORR2] iexp =[];[exportexperimentaldata] eexp =[];[exportexperimentaldata] Cmbulkh 2[denebulkconcentrationforhydrogen] Cmbulko 2[denebulkconcentrationforoxygen] ko =2 : 63 10 )]TJ/F15 11.9552 Tf 7.084 -4.339 Td [(2;[RateconstantforORR] kh =3 : 6 10 )]TJ/F15 11.9552 Tf 7.085 -4.339 Td [(4;[RateconstantforHOR] O = ko exp )]TJ/F15 11.9552 Tf 9.299 0 Td [( o FV = RT ;[KineticexpressionforORR] H = kh exp )]TJ/F15 11.9552 Tf 9.298 0 Td [( h FV = RT ;[KineticexpressionforHOR] =[ O= O + H ];[Surfacecoverageofhydrogenperoxide] a = :=ilimh 2 o 2 )]TJ/F15 11.9552 Tf 11.955 0 Td [( :=ilimo 2; b = :=ilimh 2 o 2 )]TJ/F15 11.9552 Tf 11.955 0 Td [( :=B )]TJ/F15 11.9552 Tf 11.955 0 Td [( :=C )]TJ/F15 11.9552 Tf 11.956 0 Td [( :=ilimo 2; 157

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c =1 :=C ; theta 1= b + sqrt b: 2 +4 : c: a := a ; ih 2= A: ilimh 2 := A + ilimh 2; figure plot ih 2 ;V; 0 + 0 ; io 2= B: ilimo 2 : )]TJ/F22 11.9552 Tf 11.955 0 Td [(theta 2 := B: )]TJ/F22 11.9552 Tf 11.956 0 Td [(theta 2+ ilimo 2; ih 2 o 2= C: ilimh 2 o 2 : theta 2 := C: theta 2+ ilimh 2 o 2; iT = ih 2+ io 2+ ih 2 o 2;[Totalcurrent] w = )]TJ/F15 11.9552 Tf 9.298 0 Td [(6: : 05:6;[Frequencyrange] w =10 : w ; Kh 2= w delta 2 =dh 2; bh 2= tanh sqrt i Kh 2 := sqrt i Kh 2; Ko 2= w: delta 2 =do 2; bo 2= tanh sqrt i Ko 2 := sqrt i Ko 2; Kh 2 o 2= w: delta 2 =dh 2 o 2; b 2 o 2= tanh sqrt i Kh 2 o 2 := sqrt i Kh 2 o 2; C 1=1 := RtH 2+ ZDH 2 bh 2; D 1=1 := RtO 2+ ZDO 2 bo 2; D 2=1 := RtO 2+ ZDO 2 bo 2 : )]TJ/F22 11.9552 Tf 11.955 0 Td [(gamma ; E 1=1 := RtH 2 O 2+ ZDH 2 O 2 b 2 o 2; E 2=1 := RtH 2 O 2+ ZDH 2 O 2 b 2 o 2 : gamma ; H = D 2 )]TJ/F22 11.9552 Tf 11.956 0 Td [(E 2 : D 1 )]TJ/F22 11.9552 Tf 11.955 0 Td [(E 1 := 96500 i 2 3 : 14 w )]TJ/F22 11.9552 Tf 11.955 0 Td [(D 2+ E 2; z = re + := C 1+ D 1+ E 1+ H + i 2 3 : 14 w c + := C 1+ i 2 3 : 14 w c ; zr = real z ; zi = imag z ; 158

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APPENDIXC:COMPUTATIONALALGORITHMFORMODEL3 r 1=0 : 135;[Electrolyteresistance] c =0 : 212;[Double-layercapacitance] o =0 : 5[symmetrycoecientforORR] h = )]TJ/F22 11.9552 Tf 11.955 0 Td [( o ;[symmetrycoecientforHOR] V =0 : 68;[operatingvoltage] F =96500;[Faradaysconstant] R =8 : 314;[Universalgasconstant] T =298;[Temperature] ko =2 : 63 10 )]TJ/F15 11.9552 Tf 7.084 -4.339 Td [(2;[RateconstantforORR] kh =3 : 6 10 )]TJ/F15 11.9552 Tf 7.085 -4.338 Td [(4;[RateconstantforHOR] O = ko exp )]TJ/F15 11.9552 Tf 9.299 0 Td [( o FV = RT ;[KineticexpressionforORR] H = kh exp )]TJ/F15 11.9552 Tf 9.298 0 Td [( h FV = RT ;[KineticexpressionforHOR] =[ O= O + H ];[Surfacecoverageofhydrogenperoxide] A =2 : Kh 2 : F: Dh 2 : Cmbulkh 2 : exp bh 2 : vh 2; k 1=4 : F: Do 2 : Cmbulko 2 : exp )]TJ/F22 11.9552 Tf 9.299 0 Td [(bo 2 : vo 2; C 1= Kptf: exp bpt: vpt ; C 2= )]TJ/F22 11.9552 Tf 9.299 0 Td [(Kptb: exp )]TJ/F22 11.9552 Tf 9.299 0 Td [(bpt: vpt ; k 2= C 1 )]TJ/F22 11.9552 Tf 11.955 0 Td [(C 2+ k 3; a = Kpt: k 1 : ilimo 2+ C 1+ C 1 : ilimo 2; b = )]TJ/F15 11.9552 Tf 9.298 0 Td [( Kpt: k 1 : ilimo 2+ k 2+ k 2 )]TJ/F15 11.9552 Tf 11.955 0 Td [( Kpto: k 1 : ilimo 2; c = k 2 : k 1 : Kpt )]TJ/F22 11.9552 Tf 11.955 0 Td [(Kpto ; theta 1= b + sqrt b: 2 )]TJ/F15 11.9552 Tf 11.955 0 Td [( : c: a := a ; theta 2= C 1 := k 2; figure plot V;theta 2; ih 2= A: ilimh 2 := A + ilimh 2; Ke = Kpt + Kpto )]TJ/F22 11.9552 Tf 11.955 0 Td [(Kpt : theta 2; B = Ke: k 1; io 2= B: ilimo 2 := B + ilimo 2; ipt = C 1 : )]TJ/F22 11.9552 Tf 11.955 0 Td [(theta 2 )]TJ/F15 11.9552 Tf 11.956 0 Td [( C 2 : theta 2; 159

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iT = io 2+ ipt ; na = log iT := Kh 2 : Cmbulkh 2 : )]TJ/F15 11.9552 Tf 11.955 0 Td [( iT:=ilimh 2 :=bh 2; VT = V )]TJ/F15 11.9552 Tf 11.955 0 Td [( iT: Reff )]TJ/F22 11.9552 Tf 11.955 0 Td [(na ; y =[ VT ; iT ; theta 2]; w = )]TJ/F15 11.9552 Tf 9.298 0 Td [(6: : 05:6;[Frequencyrange] w =10 : w ; Ko 2= w: delta 2 =do 2; bo 2= tanh sqrt i Ko 2 := sqrt i Ko 2; C 1=1 := RtH 2+ ZDH 2 bh 2; A 1=1 := RtO 2+ ZDO 2 bo 2; A 2=1 : g 2 := RtO 2+ ZDO 2 bo 2; B 1=1 : :=RtPtf + :=RtPtb ; B 2=1 : f 3+ f 4; T = A 2+ B 2 : A 1 )]TJ/F22 11.9552 Tf 11.955 0 Td [(B 1 := 96500 i 2 3 : 14 w )]TJ/F22 11.9552 Tf 11.956 0 Td [(B 2+ A 2+ f 5; z = re + := A 1+ B 1+ C 1+ T + i 2 3 : 14 w c + := A 1+ i 2 3 : 14 w c ; zr = real z ; zi = imag z ; 160

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Kramers-KronigRelations," JournaloftheElectrochemicalSociety 142 4159{4168. [127]M.E.Orazem,ASystematicApproachtowardErrorStructureIdentication forImpedanceSpectroscopy," JournalofElectroanalyticalChemistry 572 317{327. [128]R.deL.Kronig,OntheTheoryofDispersionofX-Rays," JournaloftheOptical SocietyofAmericaandReviewofScienticInstruments 12 547{557. [129]R.deL.Kronig,DispersionstheorieimRontgengebeit," PhysikZeitschrift 30 521{522. [130]H.A.Kramers,DieDispersionundAbsorptionvonRontgenstrahlen," Physik Zeitschrift 30 522{523. [131]P.Agarwal,M.E.Orazem,andL.H.Garca-Rubio,ApplicationoftheKramers KronigRelationstoElectrochemicalImpedanceSpectroscopy,"in Electrochemical Impedance:AnalysisandInterpretation ,J.Scully,D.Silverman,andM.Kendig, editors,volumeASTMSTP1188Philadelphia,PA:AmericanSocietyforTesting andMaterials,1993115{139. [132]B.A.BoukampandJ.R.Macdonald,AlternativestoKronig-KramersTransformationandTesting,andEstimationofDistribtuions," SolidStateIonics 74 85{101. [133]B.A.Boukamp,ALinearKronig-KramersTransformTestforImmittanceData Validation," JournaloftheElectrochemicalSociety 142 1885{1894. [134]P.K.Shukla,M.E.Orazem,andO.D.Crisalle,ValidationoftheMeasurement ModelConceptforErrorStructureIdentication," ElectrochimicaActa 49 2881{2889. [135]M.E.Orazem,P.Agarwal,C.Deslouis,andB.Tribollet,ApplicationofMeasurementModelstoElectro-HydrodynamicImpedanceSpectroscopy," Journalofthe ElectrochemicalSociety 143 948{960. [136]M.E.Orazem,M.Durbha,C.Deslouis,H.Takenouti,andB.Tribollet,Inuence ofSurfacePhenomenaontheImpedanceResponseofaRotatingDiskElectrode," ElectrochimicaActa 44 4403{4412. [137]I.Frateur,C.Deslouis,M.E.Orazem,andB.Tribollet,ModelingoftheCast Iron/DrinkingWaterSystembyElectrochemicalImpedanceSpectroscopy," ElectrochimicaActa 44 4345{4356. [138]C.Deslouis,T.E.Moustad,M.M.Musiani,M.E.Orazem,V.Provost,and B.Tribollet,EectofCationsonTheDiusivityofTheChargeCarriersin PolyanilineMembranes," ElectrochimicaActa 44 2087{2093. 171

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[139]P.M.GomadamandJ.W.Weidner,AnalysisofElectrochemicalImpedance SpectroscopyinProtonExchangeMembraneFuelCells," InternationalJournalof EnergyResearch 29 1133{1151. [140]T.E.SpringerandI.D.Raistrick,ElectricalImpedanceofPoreWallforthe Flooded-AgglomerateModelofPorousGasDiusionElectrodes," Journalofthe ElectrochemicalSociety 136 1594{1603. [141]F.JaouenandG.Lindberg,TransientTechniquesforInvestigatingMassTransport LimitationsinGasDiusionElectrodes1.ModelingofthePEFCCathode," Journal oftheElectrochemicalSociety 150 A1699{A1710. [142]Q.Guo,M.Gayetano,Y.Tsou,E.S.D.Castro,andR.E.White,Studyof IonicConductivityProlesofTheAirCathodeofAPEMFCbyACImpedance Spectroscopy," JournaloftheElectrochemicalSociety 151 A1440{A1449. [143]H.F.Oetjen,V.M.Schmidt,U.Stimming,andF.Trila,PerformanceDataofa ProtonExchangeMembraneFuelCellUsingH2/COasFuelGas," Journalofthe ElectrochemicalSociety 143 3838{3842. [144]O.Antoine,Y.Bultel,andR.Durand,OxygenReductionReactionKineticsand MechanismonPlatinumNanoparticlesInsideNaon," JournalofElectroanalytical Chemistry 499 85{94. [145]K.Wiezell,P.Gode,andG.Lindbergh,SteadyStateandEISInvestigations ofHydrogenElectrodesandMembranesinPolymerElectrolyteFuelCells-I. Modeling," JournaloftheElectrochemicalSociety 153 A749{A758. [146]X.Cheng,L.Chen,C.Peng,Z.Chen,Y.Zhang,andQ.Fan,CatalystMicrostructureExaminationofPEMFCMembrane," JournaloftheElectrochemicalSociety 151 A48{A52. [147]A.A.Kulikovsky,Quasi-3DModelingofwatertransportinPolymerElectrolyte FuelCells," JournaloftheElectrochemicalSociety 150 A1432{A1439. [148]P.Berg,K.Promislow,J.S.Pierre,J.Stumper,andB.Wetton,WaterManagementinPEMFuelCells," JournaloftheElectrochemicalSociety 151 A341{A353. [149]A.Su,F.Weng,C.Hsu,andY.Chen,StudiesonFloodinginPEMFuelCell CathodeChannels," InternationalJournalofHydrogenEnergy 31 1031{ 1039. [150]W.He,J.S.Yi,andT.V.Nguyen,Two-PhaseFlowModeloftheCathodeof PEMFuelCellsusingInterdigitatedFlowFields," AICHE 46 2053{2064. [151]S.W.Cha,R.Hayre,Y.Park,andF.B.Prinz,Electrochemicalimpedance investigationofoddinginmicro-owchannelsforprotonexchangemembranefuel cells," JournalofPowerSources 161 138{142. 172

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[152]F.Barbir,H.Gorgun,andX.Wang,RelationshipBetweenPressureDropandCell ResistanceasaDiagnosticToolforPEMFuelCells," JournalofPowerSources 141 96{101. [153]S.GeandC.-Y.Wang,LiquidWaterFormationandTrasnportinPEFCAnode," JournaloftheElectrochemicalSociety 154 B998{B1005. [154]I.A.Schneider,H.Kuhn,A.Wokaun,andG.G.Scherer,Fastlocallyresolved electrochemicalimpedancespectroscopyinpolymerelectrolytefuelcells," Journalof theElectrochemicalSociety 152 A2092{A2103. [155]I.A.Schneider,H.Kuhn,A.Wokaun,andG.G.Scherer,Spatiallyresolved characterizationofPEFCsusingsimultaneouslyneutronradiographyandlocally resolvedimpedancespectroscopy," ElectrochemistryCommunications 7 1393{1397. [156]I.A.Schneider,H.Kuhn,A.Wokaun,andG.G.Scherer,StudyofWaterBalance inaPolymerElectrolyteFuelCellbyLocallyResolvedImpedanceSpectroscopy," JournaloftheElectrochemicalSociety 152 A2383{A2389. [157]N.Fouquet,C.Doulet,C.Nouillant,G.Dauphin-Tanguy,andB.Ould-Bouamama, ModelbasedPEMfuelcellstate-of-healthmonitoringviaacimpedancemeasurements," JournalofPowerSources 159 905{913. [158]G.J.Brug,A.L.G.vandenEeden,M.Sluyters-Rehbach,andJ.H.Sluyters,The AnalysisofElectrodeImpedancesComplicatedbythePresenceofaConstantPhase Element," JournalofElectroanalyticChemistry 176 275{295. [159]J.R.Macdonald,editor, ImpedanceSpectroscopy:EmphasizingSolidMaterialsand Systems NewYork:JohnWiley&Sons,1987. [160]A.Lasia,ElectrochemicalImpedanceSpectroscopyanditsApplications,"in ModernAspectsofElectrochemistry ,R.E.White,B.E.Conway,andJ.O.Bockris, editors,volume32NewYork,NewYork:PlenumPress,1999143{248. [161]Z.Lukacs,TheNumericalEvaluationoftheDistortionofEISDataduetothe DistributionofParameters," JournalofElectroanalyticalChemistry 432 79{83. [162]Z.Lukacs,EvaluationofModelandDispersionParametersandTheirEectson theFormationofConstant-PhaseElementsinEquivalentCircuits," Journalof ElectroanalyticalChemistry 464 68{75. [163]J.R.Macdonald,GeneralizationsofUniversalDielectricResponseandaGeneral Distribution-of-Activation-EnergiesModelforDielectricandConductingSystems," JournalofAppliedPhysics 58 1971{1978. 173

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[164]J.R.Macdonald,FrequencyResponseofUniedDielectricandConductive SystemsInvolvinganExponentialDistributionofActivationEnergies," Journalof AppliedPhysics 58 1955{1970. [165]R.L.HurtandJ.R.Macdonald,DistributedCircuitElementsinImpedance Spectroscopy:AUniedTreatmentofConductiveandDielectricSystems," Solid StateIonics 20 111{124. [166]J.R.Macdonald,LinearRelaxation:Distributions,ThermalActivation,Structure, andAmbiguity," JournalofAppliedPhysics 62 R51{R62. [167]J.R.Macdonald,Power-LawExponentsandHiddenBulkRelaxationinthe ImpedanceSpectroscopyofSolids," JournalofElectroanalyticalChemistry 378 17{29. [168]Z.KernerandT.Pajkossy,impedanceofroughcapacitiveelectrode:roleofsurface disorder," JournalofElectroanalyticalChemistry 448 139{142. [169]C.HitzandA.Lasia,ExperimentalstudyandmodelingonimpedanceofHERon porousNielectrode," JournalofElectroanalyticalChemistry 500 213{222. [170]J.-B.Jorcin,M.E.Orazem,N.Pebere,andB.Tribollet,CPEAnalysisbyLocal ElectrochemicalImpedanceSpectroscopy," ElectrochimicaActa 51 1473{ 1479. [171]V.M.-W.Huang,V.Vivier,M.E.Orazem,N.Pebere,andB.Tribollet,The ApparentCPEBehaviorofaDiskElectrodewithFaradaicReactions," Journalof theElectrochemicalSociety 154 C99{C107. [172]M.Mazurek,N.Benker,C.Roth,T.Buhrmester,andH.Fuess,Electrochemical ImpedanceandX-RayAbsorptionSpectroscopyEXAFSasIn-SituMethodsto studythePEMFCAnode," FuelCells 1 16{20. [173]A.-K.Meland,S.Kjelstrup,andD.Bedeaux,RateLimitingProtonHydration intheAnodeofthePEMFuelCell," JournalofMembraneScience 282 96{108. [174]J.Labato,M.A.Rodrigo,J.Linares,andK.Scott,EectoftheCatalyticInk PreparationMethodonthePerformanceofHighTemperaturePEMFuelCells," JournalofPowerSources 157 284{292. [175]K.-T.Jeng,C.-C.Chien,N.-Y.Hsu,W.-M.Huang,S.-D.Chiou,andS.-H.Lin, FabricationandinpedancestudiesofDMFCanodeincorporatedwithCNTsupportedhighmetalcontentelectrocatalyst," JournalofPowerSources 2007 33{41. [176]A.BieberleandL.J.Gauckler,ReactionMmechanismofNipatternanodesfor SOFC," SolidStateIonics 135 337{345. 174

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[177]N.-Y.Hsu,S.-C.Yen,K.-T.Jeng,andC.-C.Chien,ImpedanceStudiesand ModelingofDirectMethanolFuelCellAnodewithInterfaceandPorousStructure Perspectives," JournalofPowerSources 161 232{239. [178]S.-S.Hsieh,S.-H.Yang,andC.-L.Feng,Characterizationoftheoperational parametersofaH2-airmicroPEMFCwithdierentoweldsbyimpedance spectroscopy," JournalofPowerSources 162 262{270. [179]S.K.RoyandM.E.Orazem,GraphicalEstimationofInterfacialCapacitanceof PEMFuelCellsfromImpedanceMeasurements," JournaloftheElectrochemical Society xxx submitted. [180]B.Andreaus,A.J.McEvoy,andG.G.Scherer,AnalysisofPerformanceLosses inPolymerElectrolyteFuelCellsatHighCurrentDensitiesbyImpedanceSpectroscopy," ElectochimicaActa 47 2223{2229. [181]M.Ciureanu,EectsofNaondehydrationinPEMfuelcells," JournalofApplied Electrochemistry 34 705{714. [182]A.G.Hombrados,L.Gonzalez,M.A.Rubio,W.Agila,E.Villanueva,D.Guinea, E.Chinarro,B.Moreno,andJ.R.Jurado,SymmetricalElectrodeModefor PEMFCCharacterizationusingImpedanceSpectroscopy," JournalofPower Sources 151 25{31. [183]T.Abe,H.Shima,K.Watanabe,andY.Ito,StudyofPEFCsbyACImpedance, CurrentInterrupt,andDewPointMeasurementsI.EectofHumidityinOxygen Gas," JournaloftheElectrochemicalSociety 151 A101{A105. [184]S.v.Kraemer,M.Puchner,P.Jannasch,A.Lundblad,andG.Lindbergh,Gas DiusionElectrodesandMembraneElectrodeAssembliesBasedonaSulfonated PolysulfoneforHigh-TemperaturePEMFC," JournaloftheElectrochemicalSociety 153 A2077{A2084. [185]M.CiureanuandR.Roberge,ElectrochemicalImpedanceStudyofPEMFuel Cells.ExperimentalDiagnosticandModelingofAirCathode," JournalofPhysical ChemistryB 105 3531{3539. [186]T.Romero-Castana,L.G.Arriaga,andU.Cano-Castillo,ImpedanceSpectroscopy asaToolintheEvaluationofMEA," JournalofPowerSources 118 179{ 182. [187]N.WagnerandM.Schulze,ChangeofElectrochemicalImpedanceSpectraduring COPoisoningofthePtandPt-RuAnodesinaMembraneFuelCellPEFC," ElectochimicaActa 48 3899{3907. [188]N.WagnerandE.Glzow,ChangeofelectrochemicalimpedancespectraEISwith timeduringCO-poisoningofthePt-anodeinamembranefuelcell," Journalof PowerSources 127 341{347. 175

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[189]M.N.Tsampas,A.Pikos,S.Brosda,A.Katsaounis,andC.G.Vayenas,TheEect ofMembraneThicknessontheConductivityofNaon," ElectochimicaActa 51 2743{2755. [190]E.H.Sanders,K.A.McGradya,G.E.Wneka,C.A.Edmondsonb,J.M.Mueller, J.J.Fontanella,S.Suarez,andS.G.Greenbaum,CharacterizationofElectrosprayedNaonFilms," JournalofPowerSources 129 55{61. [191]F.Liu,B.Yi,D.Xing,J.Yu,Z.Hou,andY.Fu,DevelopmentofNovelSelfHumidifyingCompositeMembranesforFuelCells," JournalofPowerSources 124 81{89. [192]V.Ramani,J.M.Fenton,H.R.Kunz,andK.R.Cooper, ExperimentalMethods andDataAnalysesforPolymerElectrolyteFuelCells SouthernPines,NC:Scribner Associates,Inc.,2005. [193]D.A.Blom,J.R.Dunlap,T.A.Nolan,andL.F.Allarda,PreparationofCrossSectionalSamplesofProtonExchangeMembraneFuelCellsbyUltramicrotomyfor TEM," JournaloftheElectrochemicalSociety 150 A414{A418. [194]S.K.RoyandM.E.Orazem,ErrorAnalysisoftheImpedanceResponseofPEM FuelCells," JournaloftheElectrochemicalSociety 154 B883{B891. [195]A.Z.WeberandJ.Newman,TransportinPolymer-ElectrolyteMembranes2. MathematicalModels," JournaloftheElectrochemicalSociety 151 A311{ A325. [196]F.Y.Zhang,X.G.Yang,andC.Y.Wang,LiquidwaterremovalfromaPEMfuel cell," JournaloftheElectrochemicalSociety 153 A225{A232. [197]X.Cheng,J.Zhang,Y.Tang,C.Song,J.Shen,D.Song,andJ.Zhang,Hydrogen crossoverinhigh-temperaturePEMfuelcell," JournalofPowerSources 167 25{31. [198]M.C.Leverett,CapillaryBehaviorinporoussolid,"in Pet.Trans.AIME ,volume 142152. [199]X.LiandI.Sabir,ReviewofBipolarPlatesinPEMFuelCells:Flow-Field Designs," InternationalJournalofHydrogenEnergy 30 359{371. [200]S.Hsieh,S.Yang,J.Kuo,C.Huang,andH.Tsai,StudyofOperationalParametersonthePerformanceofMicroPEMFCswithDierentFlowFields," Energy ConversionandManagement 47 1868{1878. [201]A.deSouzaandE.R.Gonzalez,Inuenceoftheoperationalparametersonthe performanceofpolymerelectrolytemembranefuelcellswithdierentowelds," J SolidStateElectrochem 7 651{657. 176

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[202]A.Su,Y.C.Chiu,andF.B.Weng,TheImpactofFlowFieldPatternonConcentrationandPerformanceinPEMFC," InternationalJournalofEnergyResearch 29 409{425. [203]Y.Yoon,W.Lee,G.Park,T.Yang,andC.Kim,EectsofChannelCongurations ofFlowFieldPlatesonthePerformanceofaPEMFC," ElectochimicaActa 50 709{712. [204]S.Dutta,S.Shimpalee,andJ.W.V.Zee,Three-DimensionalNumericalSimulationofStraightChannelPEMFuelCell," JournalofAppliedElectrochemistry 30 135{146. [205]W.k.Lee,S.Shimpalee,andJ.W.V.Zee,VerifyingPredictionsofWaterand CurrentDistributionsinaSerpentineFlowFieldPolymerElectrolyteMembrane," JournalofTheElectrochemicalSociety 150 A341{A348. [206]A.Kazim,H.T.Liu,andP.Forges,ModelingofPerformanceofPEMFuelCells withConventionalandInterdigitatedFlowFields," JournalofAppliedElectrochemistry 29 1409{1416. [207]T.V.Nguyen,AGasDistributorDesignforProton-Exchange-MembraneFuel Cells," JournaloftheElectrochemicalSociety 143 L103. [208]R.Makharia,M.F.Mathias,andD.R.Baker,MeasurementofCatalystLayer ElectrolyteResistanceinPEFCsusingElectrochemicalImpedanceSpectroscopy," JournaloftheElectrochemicalSociety 152 A970{A977. [209]Y.Bultel,L.Genies,O.Antoine,P.Ozil,andR.Durand,ModelingImpedance DiagramsofActiveLayersinGasDiusionElectrodes:Diusion,OhmicDrop EectsandMultistepReactions," JournalofElectroanalyticalChemistry 527 143{155. [210]M.E.Orazem,T.E.Moustad,C.Deslouis,andB.Tribollet,TheErrorStructure ofImpedanceSpectroscopyMeasurementsforSystemswithaLargeOhmicResistancewithRespecttothePolarizationImpedance," JournaloftheElectrochemical Society 143 3880{3890. [211]S.K.RoyandM.E.Orazem,UseofDeterministicImpedanceModelsforInterpretationofLow-FrequencyInductiveLoopsinPEMFuelCells," ECST-Proton ExchangeMembraneFuelCells6 3 1031{1040. [212]I.Epelboin,M.Keddam,andJ.C.Lestrade,Faradaicimpedanceandintermediatesinelectrochemicalreactions," FaradayDiscussions 56 264{275. [213]R.D.Armastron,R.E.Firman,andH.R.Thirsk,ACImpedanceofcomplex eelctrochemicalreactions," FaradayDiscussions 56 244{263. [214]R.D.ArmstrongandK.Edmondson,Theimpedanceofmetalsinthepassiveand transpassiveregions," ElectochimicaActa 18 937{943. 177

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[215]H.Xu,R.Kunz,andJ.M.Fenton,InvestigationofPlatinumOxidationinPEM FuelCellsatVariousRH," ElectrochemicalandSolid-StateLetters 10 B1{B5. [216]Y.Bultel,K.Wiezell,F.Jaouen,P.Ozil,andG.Lindberg,Investigationofmass transportingasdiusionlayerattheaircathodeofaPEMFC," ElectochimicaActa 51 474{488. [217]K.Wiezell,P.Gode,andG.Lindbergh,Steady-stateandEISInvestigationsof hydrogenelectrodesandmembranesinthePolymerElectrolyteFuelCells," Journal oftheElectrochemicalSociety 153 A759{A764. [218]M.E.OrazemandB.Tribollet,AnIntegratedApproachtoElectrochemical ImpedanceSpectroscopy," ElectrochimicaActa ,submitted. [219]S.K.Roy,M.E.Orazem,andB.Tribollet,InterpretationofLow-Frequency InductiveLoopsinPEMFuelCells," JournaloftheElectrochemicalSociety 154 B1378{B1388. [220]R.B.Shumbera,H.H.Kan,andJ.F.Weaver,OxidationofPt-hex-R0.7by gas-phaseoxygenatoms," SurfaceScience 601 235{246. [221]P.Agarwal,M.E.Orazem,andL.H.Garca-Rubio,MeasurementModelsFor ElectrochemicalImpedanceSpectroscopy:3.EvaluationofConsistencywiththe Kramers-KronigRelations," JournaloftheElectrochemicalSociety 142 4159{4156. [222]M.E.Orazem,AsystematicApproachTowardErrorStructureIdentication forImpedanceSpsectroscopy," JournalofElectroanalyticChemistry 572 317{327. [223]M.Durbha,M.E.Orazem,andL.H.Garca-Rubio,SpectroscopyApplications oftheKramers-KronigRelations:ImplicationsforErrorStructureIdentication," JournaloftheElectrochemicalSociety 144 48{55. [224]M.E.Orazem,N.Pebere,andB.Tribollet,ANewLookatGraphicalRepresentationofImpedanceData," JournaloftheElectrochemicalSociety 153 B129{B136. [225]S.K.RoyandM.E.Orazem,AnalysisofFloodingasaStochasticProcessinPEM FuelCellsbyImpedanceTechniques," JournalofPowerSources ,inpress. [226]C.H.HsuandF.Mansfeld,TechnicalNote:ConcerningtheConversionofthe ConstantPhaseElementParameter Y 0 intoaCapacitance," Corrosion 57 747{748. [227]G.J.Brug,A.L.G.vandenEeden,M.Sluyters-Rehbach,andJ.H.Sluyters,The AnalysisofElectrodeImpedanceComplicatedbythePresenceofaConstantPhase Elementt," J.Electroanal.Chem. 176 275{295. 178

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[228]S.P.HarringtonandT.M.Devine,AnalysisofElectrodesDisplayingFrequency DispersioninMott-SchottkyTests," JournaloftheElectrochemicalSociety 155 C381{C386. [229]P.Zoltowski,OntheElectricalCapacitanceofInterfacesExhibitingConstant PhaseElementBehavior," JournalofElectroanalyticalChemistry 443 149{154. 179

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BIOGRAPHICALSKETCH SunilwasbornandraisedinBihar,astateincentral-easternIndia,famousforits agriculturalproduction,educationalheritageandasthebirthplaceofseveralreligions includingBuddhism. HereceivedaBSdegreeinchemicalengineeringfromtheNationalInstituteofTechnology,Surat,India,inMay2002,andcompletedanMSdegreeinchemicalengineeringin July2004fromtheprestigiousIndianInstituteofTechnology,Kharagpur.InhisMSresearch,hedesignedaspraydryerforcosteectivedryingAloeveragel,characterizedthe gel,anddriedpowdertoconstituteskincareproducts,sponsoredbyEmamiInc.,India. SunilthenjoinedthePh.D.programintheDepartmentofChemicalEngineeringatthe UniversityofFloridaUFinfall2004.Hisdoctoralresearch,sponsoredbyNASA,investigatedseveralfactorsrelatedtosidereactionsandintermediates,andoodinganddrying ofthefuelcellresponsiblefordegradationintheperformanceandlifetime,whichare themajorhurdlesinthecommercializationofthefuelcell.Hisresearchinterestsinclude appliedelectrochemistrysuchasfuelcell,battery,semiconductor,andnanotechnology. Sunilhaspublished5journalarticlesand3proceedingpapers.Heisarefereeto JournalofElectrochemicalSocietysince2005,andhasservedasanelectedPresidentof theStudentChapterofTheElectrochemicalSocietyattheUniversityofFloridain200607.Sunilreceivedthe2008IEEEDivisionH.H.DowMemorialStudentAchievement AwardfromTheElectrochemicalSociety. 180